chapter 11 length and area. 11.1 areas of triangles and parallelograms area of a square = s 2 area...
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![Page 1: Chapter 11 Length and Area. 11.1 Areas of Triangles and Parallelograms Area of a square = s 2 Area of a rectangle = bh Area of a parallelogram = bh Area](https://reader033.vdocument.in/reader033/viewer/2022061616/56649ddd5503460f94ad4bcf/html5/thumbnails/1.jpg)
Chapter 11Length and Area
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11.1 Areas of Triangles and Parallelograms•Area of a square = s2
•Area of a rectangle = bh•Area of a parallelogram = bh•Area of a triangle = bh
2
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Important Information
•If two polygons are congruent, then they have the same area.
•The area of a region is the sum of the areas of its non-overlapping parts.
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11.2 Areas of Trapezoids, Rhombuses, and Kites
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Formulas
•Area of a trapezoid = h(b1 + b2) 2
•Area of a rhombus = d1 d2
2
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More Formulas
•Area of a kite = d1 d2
2
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Examples•Find the area of RSTU.•Find the area of the polygon
RSTWUV.
28
35
2520
W
VU T
SR
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Example
•One diagonal of a kite is 1/3 as long as the other. The area of the kite is 0.24m2. What are the lengths of the diagonals?
![Page 9: Chapter 11 Length and Area. 11.1 Areas of Triangles and Parallelograms Area of a square = s 2 Area of a rectangle = bh Area of a parallelogram = bh Area](https://reader033.vdocument.in/reader033/viewer/2022061616/56649ddd5503460f94ad4bcf/html5/thumbnails/9.jpg)
11.3 Perimeter and Area of Similar Figures
•If two polygons are similar with the lengths of corresponding sides in the ratio a:b, then the ratio of their areas is a2:b2.
![Page 10: Chapter 11 Length and Area. 11.1 Areas of Triangles and Parallelograms Area of a square = s 2 Area of a rectangle = bh Area of a parallelogram = bh Area](https://reader033.vdocument.in/reader033/viewer/2022061616/56649ddd5503460f94ad4bcf/html5/thumbnails/10.jpg)
Example
•ABCD is similar to RSTU.•Find the ratio of the perimeters.•Find the ratio of the areas.
1018
B C
A D
S
R U
T
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Example
You are painting 2 wall in an office complex that are similar in shape- both rectangles. One wall has a side length of 10ft. The corresponding side of the other wall is 14ft. You need 7 quarts to paint the larger wall. How many quart do you need for the smaller wall?
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Example
•The Pentagon in Washington DC is a regular pentagon with side lengths of 900ft. The area is 1,400,000ft2. The perimeter of a scale model of the building is 30yds. What is the area of the scale model?
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11.4 Circumference and Arc length•Circumference – the distance around the
circle
C = 2r = dr
d
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•Arc length- a portion of the circumference of a circle
= mAB
360arc length AB
2r
r
P B
A
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Find the length of AB
•1. 2.
45
9in.
P B
A
90
15in.
P B
A
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Find the indicated measures.
• Find the circumference.
756.82cm
T
Find the mAB.
r = 15.28 ft.
AB = 40ft.
B
A
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11.5 Area of Circles and Sectors•Area of a circle A = πr2
•Sector of a circle- region bounded by 2 radii of the circle and the intercepted arc.
•Sector APB = m AB πr2 360o
r
P
A
B
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Example
•Find the area of the sectors formed by <HJK.
100
12cm
J
H
K
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Example
•Find the area between the large outer circle and the two smaller circles.
3m
![Page 20: Chapter 11 Length and Area. 11.1 Areas of Triangles and Parallelograms Area of a square = s 2 Area of a rectangle = bh Area of a parallelogram = bh Area](https://reader033.vdocument.in/reader033/viewer/2022061616/56649ddd5503460f94ad4bcf/html5/thumbnails/20.jpg)
11.6 Areas of Regular Polygons
•The center of a polygon and the radius of a polygon are the center and radius of its circumscribed circle.
•Apothem of a polygon- distance from center to any side of a polygon
•Central Angle of a regular polygon- the angle formed by 2 radii drawn to consecutive vertices of the polygon
![Page 21: Chapter 11 Length and Area. 11.1 Areas of Triangles and Parallelograms Area of a square = s 2 Area of a rectangle = bh Area of a parallelogram = bh Area](https://reader033.vdocument.in/reader033/viewer/2022061616/56649ddd5503460f94ad4bcf/html5/thumbnails/21.jpg)
Vocabulary
•Apothem
•Radius
•Central AngleN
M
P
Q
![Page 22: Chapter 11 Length and Area. 11.1 Areas of Triangles and Parallelograms Area of a square = s 2 Area of a rectangle = bh Area of a parallelogram = bh Area](https://reader033.vdocument.in/reader033/viewer/2022061616/56649ddd5503460f94ad4bcf/html5/thumbnails/22.jpg)
Formula
•Area of a regular polygon A =
N
M
P
Q
![Page 23: Chapter 11 Length and Area. 11.1 Areas of Triangles and Parallelograms Area of a square = s 2 Area of a rectangle = bh Area of a parallelogram = bh Area](https://reader033.vdocument.in/reader033/viewer/2022061616/56649ddd5503460f94ad4bcf/html5/thumbnails/23.jpg)
Examples
•For a regular octagon inscribed in circle C, find the following:
•m<RCY =
•m<RCZ =
•M<ZYC =
C
R
Y
Z
![Page 24: Chapter 11 Length and Area. 11.1 Areas of Triangles and Parallelograms Area of a square = s 2 Area of a rectangle = bh Area of a parallelogram = bh Area](https://reader033.vdocument.in/reader033/viewer/2022061616/56649ddd5503460f94ad4bcf/html5/thumbnails/24.jpg)
Example
•What is the area of a regular hexagon with a side length of 8 inches?
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Example
•What is the area of a regular decagon inscribed in a circle with a radius of 8mm?
![Page 26: Chapter 11 Length and Area. 11.1 Areas of Triangles and Parallelograms Area of a square = s 2 Area of a rectangle = bh Area of a parallelogram = bh Area](https://reader033.vdocument.in/reader033/viewer/2022061616/56649ddd5503460f94ad4bcf/html5/thumbnails/26.jpg)
11.7 Using Geometric Probability•Probability (of an event) - P(A)- a
measure of the likelihood that an event will occur.
•Geometric probability is a ratio that involves a geometric measure like length or area.
![Page 27: Chapter 11 Length and Area. 11.1 Areas of Triangles and Parallelograms Area of a square = s 2 Area of a rectangle = bh Area of a parallelogram = bh Area](https://reader033.vdocument.in/reader033/viewer/2022061616/56649ddd5503460f94ad4bcf/html5/thumbnails/27.jpg)
Example•Find the probability that a point chosen at
random on AE is on CD.
-4 -3 -2 -1 0 1 2 3 4 5
A B C D E
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Example
•A dart game uses targets with concentric circles of radii 5,8, and 12 inches. What is the probability the dart will earn 20 points?
20
5
15