areas of parallelograms and...
TRANSCRIPT
![Page 1: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/1.jpg)
Areas of Parallelograms and
Triangles
7-1
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Parallelogram
A parallelogram is a quadrilateral where the opposite sides are congruent and parallel.
A rectangle is a type of parallelogram, but we often see parallelograms that are not rectangles (parallelograms without right angles).
![Page 3: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/3.jpg)
Area of a Parallelogram
Any side of a parallelogram can be
considered a base. The height of a
parallelogram is the perpendicular distance
between opposite bases.
The area formula is A=bh
A=bh A=5(3) A=15m
2
![Page 4: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/4.jpg)
Area of a Triangle
A triangle is a three sided polygon. Any
side can be the base of the triangle. The
height of the triangle is the perpendicular
length from a vertex to the opposite base.
A triangle (which can be formed by splitting
a parallelogram in half) has a similar area
formula: A = ½ bh.
![Page 5: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/5.jpg)
Example
A= ½ bh A= ½ (30)(10) A= ½ (300) A= 150 km
2
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Complex Figures
Use the appropriate formula to find the area
of each piece.
Add the areas together for the total area.
![Page 7: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/7.jpg)
Example
| 27 cm |
10 cm
24 cm
Split the shape into a rectangle and triangle.
The rectangle is 24cm long and 10 cm wide.
The triangle has a base of 3 cm and a height of 10
cm.
![Page 8: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/8.jpg)
Solution
Rectangle
A = lw A = 24(10) A = 240 cm
2
Triangle A = ½ bh A = ½ (3)(10) A = ½ (30) A = 15 cm
2
Total Figure A = A1 + A2
A = 240 + 15 = 255 cm2
![Page 9: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/9.jpg)
Practice!
Pg. 353-355 # 1-14 all
# 29, 36-43 all
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7-2 The Pythagorean Theorem
and Its Converse
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Parts of a Right Triangle
In a right triangle, the side opposite the right
angle is called the hypotenuse.
It is the longest side.
The other two sides are called the legs.
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The Pythagorean Theorem
![Page 13: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/13.jpg)
Pythagorean Triples
A Pythagorean triple is a set of nonzero
whole numbers that satisfy the Pythagorean
Theorem.
Some common Pythagorean triples include:
3, 4, 5 5, 12, 13 8, 15, 17 7, 24, 25
If you multiply each number in the triple by the
same whole number, the result is another
Pythagorean triple!
![Page 14: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/14.jpg)
Finding the Length of the
Hypotenuse
What is the length of the hypotenuse of
ABC? Do the sides form a Pythagorean
triple?
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The legs of a right triangle have
lengths 10 and 24. What is the length
of the hypotenuse? Do the sides form
a Pythagorean triple?
![Page 16: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/16.jpg)
Finding the Length of a Leg
What is the value of x? Express your
answer in simplest radical form.
![Page 17: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/17.jpg)
The hypotenuse of a right triangle
has length 12. One leg has length 6.
What is the length of the other leg?
Express your answer in simplest
radical form.
![Page 18: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/18.jpg)
Triangle Classifications
Converse of the Pythagorean Theorem: If the square of the
length of the longest side of a triangle is equal to the sum of
the squares of the lengths of the other two sides, then the
triangle is a right triangle.
If c2 = a2 + b2, than ABC is a right triangle.
Theorem 8-3: If the square of the length of the longest side of a
triangle is great than the sum of the squares of the lengths of
the other two sides, then the triangle is obtuse.
If c2 > a2 + b2, than ABC is obtuse.
Theorem 8-4: If the square of the length of the longest side of a
triangle is less than the sum of the squares of the lengths of the
other two sides, then the triangle is acute.
If c2 < a2 + b2, than ABC is acute.
![Page 19: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/19.jpg)
Classifying a Triangle
Classify the following triangles as acute,
obtuse, or right.
85, 84, 13
6, 11, 14
7, 8, 9
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Practice!!
Pg. 360-363 #1-35 odd
#36-38 all, 45
# 66 5 extra credit points!
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Two Special Right Triangles
45°- 45°- 90°
30°- 60°- 90°
7-3
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45°- 45°- 90°
The 45-45-90
triangle is based
on the square
with sides of 1
unit.
1
1
1
1
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45°- 45°- 90°
If we draw the
diagonals we
form two
45-45-90
triangles.
1
1
1
1
45°
45°
45°
45°
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45°- 45°- 90°
Using the
Pythagorean
Theorem we can
find the length of
the diagonal.
1
1
1
1
45°
45°
45°
45°
![Page 25: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/25.jpg)
45°- 45°- 90°
12 + 12 = c2
1 + 1 = c2
2 = c2
2 = c
1
1
1
1
45°
45°
45°
45°
2
![Page 26: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/26.jpg)
45°- 45°- 90°
Conclusion:
the ratio of the
sides in a 45-
45-90 triangle
is
1-1-2
1
1 2
45°
45°
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45°- 45°- 90° Practice
4
4 2
SAME leg*2
4
45°
45°
![Page 28: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/28.jpg)
45°- 45°- 90° Practice
9
9 2
SAME leg*2
9
45°
45°
![Page 29: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/29.jpg)
45°- 45°- 90° Practice
2
2 2
SAME leg*2
2
45°
45°
![Page 30: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/30.jpg)
45°- 45°- 90° Practice
14
SAME leg*2
7
7
45°
45°
![Page 31: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/31.jpg)
45°- 45°- 90° Practice
![Page 32: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/32.jpg)
45°- 45°- 90° Practice
3 2
hypotenuse
2
45°
45°
![Page 33: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/33.jpg)
45°- 45°- 90° Practice
3 2
2 = 3
![Page 34: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/34.jpg)
45°- 45°- 90° Practice
3 2
hypotenuse
2
45°
45°
3 SAME
3
![Page 35: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/35.jpg)
45°- 45°- 90° Practice
6 2
hypotenuse
2
45°
45°
![Page 36: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/36.jpg)
45°- 45°- 90° Practice
6 2
2 = 6
![Page 37: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/37.jpg)
45°- 45°- 90° Practice
6 2
hypotenuse
2
45°
45°
6 SAME
6
![Page 38: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/38.jpg)
45°- 45°- 90° Practice
11 2
hypotenuse
2
45°
45°
![Page 39: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/39.jpg)
45°- 45°- 90° Practice
11 2
2 = 11
![Page 40: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/40.jpg)
45°- 45°- 90° Practice
112
hypotenuse
2
45°
45°
11 SAME
11
![Page 41: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/41.jpg)
45°- 45°- 90° Practice
8
hypotenuse
2
45°
45°
![Page 42: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/42.jpg)
45°- 45°- 90° Practice
8
2
2
2 * =
82
2 = 42
![Page 43: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/43.jpg)
45°- 45°- 90° Practice
8
hypotenuse
2
45°
45°
42 SAME
42
![Page 44: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/44.jpg)
45°- 45°- 90° Practice
4
hypotenuse
2
45°
45°
![Page 45: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/45.jpg)
45°- 45°- 90° Practice
4
2
2
2 * =
42
2 = 22
![Page 46: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/46.jpg)
45°- 45°- 90° Practice
4
hypotenuse
2
45°
45°
22 SAME
22
![Page 47: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/47.jpg)
45°- 45°- 90° Practice
6
Hypotenuse
2
45°
45°
![Page 48: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/48.jpg)
45°- 45°- 90° Practice
6
2
2
2 * =
62
2 = 32
![Page 49: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/49.jpg)
45°- 45°- 90° Practice
6
hypotenuse
2
45°
45°
32 SAME
32
![Page 50: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/50.jpg)
30°- 60°- 90°
The 30-60-90
triangle is based
on an equilateral
triangle with sides
of 2 units.
2 2
2
60° 60°
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2 2
2
60° 60°
30°- 60°- 90°
The altitude (also
the angle bisector
and median) cuts the
triangle into two
congruent triangles. 1 1
30° 30°
![Page 52: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/52.jpg)
30°
60°
This creates the
30-60-90
triangle with a
hypotenuse a
short leg and a
long leg.
30°- 60°- 90°
Short Leg
Long L
eg
![Page 53: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/53.jpg)
60°
30°
30°- 60°- 90° Practice
1
2
We saw that the
hypotenuse is
twice the short leg.
We can use the
Pythagorean
Theorem to find
the long leg.
![Page 54: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/54.jpg)
60°
30°
30°- 60°- 90° Practice
1
2 3
A2 + B2 = C2
A2 + 12 = 22
A2 + 1 = 4
A2 = 3
A = 3
![Page 55: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/55.jpg)
30°- 60°- 90°
Conclusion:
the ratio of the
sides in a 30-
60-90 triangle
is
1- 2 - 3
60°
30°
3
1
2
![Page 56: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/56.jpg)
60°
30°
30°- 60°- 90° Practice
4
8
Hypotenuse =
short leg * 2
43
The key is to find
the length of the
short side.
Long Leg =
short leg * 3
![Page 57: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/57.jpg)
60°
30°
30°- 60°- 90° Practice
5
10 Hypotenuse =
short leg * 2 53
Long Leg =
short leg * 3
![Page 58: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/58.jpg)
60°
30°
30°- 60°- 90° Practice
7
14 Hypotenuse =
short leg * 2 73
Long Leg =
short leg * 3
![Page 59: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/59.jpg)
60°
30°
30°- 60°- 90° Practice
3
23 Hypotenuse =
short leg * 2 3
Long Leg =
short leg * 3
![Page 60: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/60.jpg)
60°
30°
30°- 60°- 90° Practice
10
210 Hypotenuse =
short leg * 2
30
Long Leg =
short leg * 3
![Page 61: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/61.jpg)
30°- 60°- 90° Practice
![Page 62: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/62.jpg)
60°
30°
30°- 60°- 90° Practice
11
22 Short Leg =
Hypotenuse 2 113
Long Leg =
short leg * 3
![Page 63: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/63.jpg)
60°
30°
30°- 60°- 90° Practice
2
4 Short Leg =
Hypotenuse 2 23
Long Leg =
short leg * 3
![Page 64: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/64.jpg)
60°
30°
30°- 60°- 90° Practice
9
18 Short Leg =
Hypotenuse 2 93
Long Leg =
short leg * 3
![Page 65: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/65.jpg)
60°
30°
30°- 60°- 90° Practice
15
30 Short Leg =
Hypotenuse 2 153
Long Leg =
short leg * 3
![Page 66: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/66.jpg)
60°
30°
30°- 60°- 90° Practice
23
46 Hypotenuse =
Short Leg * 2 233
Short Leg =
Long leg 3
![Page 67: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/67.jpg)
60°
30°
30°- 60°- 90° Practice
14
28 Hypotenuse =
Short Leg * 2 143
Short Leg =
Long leg 3
![Page 68: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/68.jpg)
60°
30°
30°- 60°- 90° Practice
16
32 Hypotenuse =
Short Leg * 2 163
Short Leg =
Long leg 3
![Page 69: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/69.jpg)
60°
30°
30°- 60°- 90° Practice
3 3
63 Hypotenuse =
Short Leg * 2 9
Short Leg =
Long leg 3
![Page 70: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/70.jpg)
60°
30°
30°- 60°- 90° Practice
4 3
83 Hypotenuse =
Short Leg * 2 12
Short Leg =
Long leg 3
![Page 71: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/71.jpg)
60°
30°
30°- 60°- 90° Practice
9 3
183 Hypotenuse =
Short Leg * 2 27
Short Leg =
Long leg 3
![Page 72: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/72.jpg)
60°
30°
30°- 60°- 90° Practice
7 3
143 Hypotenuse =
Short Leg * 2 21
Short Leg =
Long leg 3
![Page 73: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/73.jpg)
60°
30°
30°- 60°- 90° Practice
113
223 Hypotenuse =
Short Leg * 2 33
Short Leg =
Long leg 3
![Page 74: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/74.jpg)
Practice!!
Pg. 369-370
# 1-30 all
#32
![Page 75: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/75.jpg)
Areas of Trapezoids, Rhombuses,
and Kites
7-4
![Page 76: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/76.jpg)
Trapezoids:
leg leg
b1 = base 1
b2 = base 2
h = height
Height – distance
between the 2 bases.
* Must be
A = ½ h(b1 + b2)
Area of
trapezoid
Height
base base
![Page 77: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/77.jpg)
Find the area of the
following trapezoid.
20in
18in
36in
30in
A = ½ h(b1 + b2)
= ½ (18in)(36in + 20in)
= ½ (18in)(56in)
= 504in2
This is the height!!
![Page 78: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/78.jpg)
Find the area of following
trapezoid.
60
5cm
7cm
A = ½ h(b1 + b2)
= ½ (3.5cm)(5cm + 7cm)
= ½ (3.5cm)(12cm)
= 20.8cm2
Need to find h first!
Short side = 2cm
h = 2√3
h = 3.5cm
This is a 30-60-90 Δ
h
![Page 79: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/79.jpg)
Area of a Rhombus or a Kite
Rhombus
4 equal sides.
Diagonals bisect each
other.
Diagonals are .
Kite
Adjacent sides are .
No sides //.
Diagonals are .
A = ½ d1d2
Area of
Kites or
Rhombi
Diagonal One Diagonal Two
![Page 80: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/80.jpg)
Find the Area of the
following Kite.
3m 3m
4m
5m
A = ½ d1d2
= ½ (6m)(9m)
=27m2
![Page 81: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/81.jpg)
Find the area of the following
Rhombus
12m
12m
b
A = ½ d1d2
= ½ (24m)(18m)
= 216m2
d1 = 24m
d2 = 18m
a2 + b2 = c2
122 + b2 = 152
144 + b2 = 225
b2 = 81
b = 9
15m
15m
![Page 82: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/82.jpg)
What have I learned??
Area of Trapezoid
A = ½ h(b1 + b2)
Area of Rhombus or Kite
A = ½ d1d2
![Page 83: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/83.jpg)
Practice!!!
Pg. 376-377 #1-35 all
![Page 84: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/84.jpg)
7-5 Area of Regular
Polygon
Apothem
![Page 85: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/85.jpg)
Find the Area of an Equilateral Triangle
Area is ½ ab a is Altitude
b is Base
34a
88
8b
316
344
8342
1
A
A
A
![Page 86: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/86.jpg)
Find the Area of an Equilateral Triangle
(there is an easier way)
Theorem
s is Side of triangle
34a
88
8b
234
1sisArea
316
3644
1
834
1 2
A
A
A
![Page 87: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/87.jpg)
Find “s” of an equilateral triangle
with area of
s is Side of triangle
234
1sisArea
325
![Page 88: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/88.jpg)
Find “s” of an equilateral triangle
with area of
s is Side of triangle
234
1sisArea
325
10
100
100
4
125
34
1325
2
2
2
s
s
s
s
s
![Page 89: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/89.jpg)
Finding the Area of a Regular
Hexagon inscribed in a circle.
Parts of the inscribed hexagon
Center
nAngleCentral
360
sidetocenterfrom
Apothem
![Page 90: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/90.jpg)
Finding the Area of a Regular
Hexagon inscribed in a circle.
Parts of the inscribed hexagon
606
360
AngleCentral
sidetocenterfrom
Apothem
30
60 60
60
![Page 91: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/91.jpg)
Finding the Area of a Regular
Hexagon inscribed in a circle.
Parts of the inscribed hexagon
606
360
AngleCentral
sidetocenterfrom
Apothem
30
60 60
60
Perimeterisp
apothemisa
apArea2
1
![Page 92: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/92.jpg)
Finding the Area of a Regular
Hexagon inscribed in a circle.
Perimeterisp
apothemisa
apArea2
1
10
1010
35
![Page 93: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/93.jpg)
Finding the Area of a Regular
Hexagon inscribed in a circle.
Perimeterisp
apothemisa
apArea2
1
10
1010
35
60106
35
Perimeter
apothem
3150
3530
60352
1
A
A
A
![Page 94: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/94.jpg)
Finding the Area of a Regular Octagon
inscribed in a circle.
Sides of 4, what the
Central Angle 4
Perimeterisp
apothemisa
apArea2
1
4
4
4
45
8
360AngleCentral
4
4
4
4
![Page 95: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/95.jpg)
How do you find the Apothem
Sides of 4 a
5.67 5.67
5.22
22
a
25.22
83.4
5.22
2
25.22
Tana
aTan
![Page 96: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/96.jpg)
Finding the Area of a Regular Octagon
inscribed in a circle.
Sides of 4, what the
Central Angle 4
Perimeterisp
apothemisa
apArea2
1
4
4 4
3248
83.4
Perimeter
apothem
45
8
360AngleCentral
4
4 4
2 2
![Page 97: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/97.jpg)
Finding the Area of a Regular Octagon
inscribed in a circle.
Sides of 4
4
Perimeterisp
apothemisa
apArea2
1
4
4
3248
83.4
Perimeter
apothem
45
8
360AngleCentral
4
4 4
2 2
28.77
3283.42
1
A
A
![Page 98: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/98.jpg)
Find the Area of a 12-gon
Sides of 1.2; Radius of 2.3
Apothem 3.2
6.022.1
a
22.2
6.03.2
6.03.2
3.26.0
22
222
222
a
a
a
a
4.14122.1 Perimeter
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Find the Area of a 12-gon
Sides of 1.2; Radius of 2.3
Apothem
4.14
22.2
p
a
776.344.1483.42
1Area
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Practice!!
Pg. 382-383
# 1-32 all
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and
Objective: Find the measures
of central angles and arcs.
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A CIRCLE is the set of all points equidistant from a given point called
the center.
This is circle P for Pacman.
Circle P
P
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A CENTRAL ANGLE of a circle is an angle with its vertex at the
center of the circle.
Central angle
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An arc is a part of a circle. In this case it is the part Pacman would
eat.
Arc
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One type of arc, a semicircle, is half of a circle.
P
A
C Semicircle ABC
m ABC = 180
B
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A minor arc is smaller than a semicircle. A major arc is greater
than a semicircle.
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R
S
P
L
N
M
RS is a minor arc.
mRS = m RPS.
O
LMN is a major arc. mLMN
=
360 – mLN
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A C
D
Identify the following in circle O:
1) the minor arcs
E O
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A C
D
Identify the following in circle O:
2) the semicircles
E O
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A C
D
Identify the following in circle O:
3) the major arcs containing point A
E O
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The measure of a central angle is equal to its intercepted
arc.
53o
53o
O P
R
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Find the measure of each arc.
1. BC = 32
2. BD = 90
3. ABC = 180
4. AB = 148
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Here is a circle graph that shows how people
really spend their time. Find the measure of
each central angle in degrees.
1. Sleep
2. Food
3. Work
4. Must Do
5. Entertainment
6. Other
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Practice!!!
Pg. 389-392 #1-14 all
# 27-41 odd and #59
*59 may be turned in for 3 extra credit points!!
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7-7 Areas of Circles and Sectors
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Quick Review
What is the circumference of a circle?
• What is the area of a circle?
• The interior angle sum of a circle is ?
• What is the arc length formula?
2r
r2
360o
mA) B
3602r
mA) B
360C
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Sector of a Circle
Formula is very similar to arc length
Notation is slightly different! - The center pt is used when describing a sector. - The is not used for sectors.
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How can we find area, based on
what we already know?
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mA) B
360r2Area of a sector =
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1. Find the area of the shaded sector 2. Find the arc length of the shaded sector.
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Segment
any ideas of how to find
the shaded area?
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Finding the Area of a Segment of a Circle
– =
Area of
Sector
Area of
Triangle
Area of
Segment minus equals
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Find the area of segment RST to the nearest hundredth.
Use formula for area of sector.
Substitute 4 for r and 90 for m.
= 4π m2
Step 1 Find the area of sector RST.
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Simplify.
Step 2 Find the area of ∆RST.
Continued
Find the area of segment RST to the nearest hundredth.
ST = 4 m, and RS = 4m.
= 8 m2
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Step 3
area of segment = area of sector RST – area of ∆RST
4.57 m2
Find the area of segment RST to the nearest hundredth.
Continued
= 4π – 8
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A segment of a circle
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Find the area of segment LNM to the nearest hundredth.
Finding the Area of a Segment
Use formula for area of sector.
Substitute 9 for r and 120 for m.
= 27π cm2
Step 1 Find the area of sector LNM.
![Page 129: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/129.jpg)
Find the area of segment LNM to the nearest hundredth.
Continued
Step 2 Find the area of ∆LNM. Draw altitude NO.
![Page 130: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/130.jpg)
Find the area of segment LNM to the nearest hundredth.
Continued
Step 3
area of segment = area of sector LNM – area of ∆LNM
= 49.75 cm2
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Find the area of the shaded portion
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Find the area of the red portion Of the Tube Sign.
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Find the shaded area with r = 2 , 4 , & 10
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1cm 3cm
5cm
What is the Area of the Black part?
![Page 135: Areas of Parallelograms and Trianglesbowmansmath.weebly.com/uploads/6/0/3/7/60377015/unit_7_area.pdfArea of a Triangle A triangle is a three sided polygon. Any side can be the base](https://reader034.vdocument.in/reader034/viewer/2022052612/5f0e67d47e708231d43f16a2/html5/thumbnails/135.jpg)
If you have 2 circles A and B that intersect at 2 points and the distance between the centers is 10. What is the area of the intersecting region?
A B
10
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Practice!!
Page 397- 398 7 - 27 odd 31-33 36-38
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7-8 Geometric Probability
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Finding a Geometric Probability
A probability is a number from 0 to 1 that
represents the chance an event will occur.
Assuming that all outcomes are equally
likely, an event with a probability of 0
CANNOT occur. An event with a
probability of 1 is just as likely to occur as
not.
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Finding Geometric probability
continued . . .
In an earlier course, you may have evaluated
probabilities by counting the number of favorable
outcomes and dividing that number by the total
number of possible outcomes. In this lesson, you
will use a related process in which the division
involves geometric measures such as length or area.
This process is called GEOMETRIC
PROBABILITY.
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Geometric Probability—
probability and length
Let AB be a segment that contains the
segment CD. If a point K on AB is chosen
at random, then the probability that that it is
on CD is as follows:
P(Point K is on CD) = Length of CD
Length of AB A
B
C
D
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Geometric Probability—
probability and AREA
Let J be a region that contains region M. If
a point K in J is chosen at random, then the
probability that it is in region M is as
follows:
P(Point K is in region M) = Area of M
Area of J J
M
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Ex. 1: Finding a Geometric
Probability
Find the geometric probability that a point
chosen at random on RS is on TU.
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Practice!!!
Pg 404-405 #1-31 ODD