integrated algebra a - lancaster high school
TRANSCRIPT
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Name______________________________ Date_______________
Integrated Algebra A Notes/Homework Packet 11
Lesson Homework
Perimeter Activity
Perimeter HW #1
Area of Rectangles & Squares HW #2
Area of Triangles HW #3
Area of Trapezoids HW #4
Area of a Shaded Region HW #5
Volume HW #6
Review
Test
2
Perimeter Activity
Perimeter Definition: _________________________________________________________
________________________________________________________________________
Show ALL WORK below for each station in the activity:
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Station 1:
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Station 2:
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Station 3:
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Station 4:
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Station 5:
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Perimeter
Perimeter is labeled in _______________, such as ______, or _______, or ________,
etc.
*Perimeter problems can be straight forward just asking you to find the perimeter
of a given diagram, such as
Example 1: Find the perimeter of the following picture.
*You could also be given information in a problem that can be used to find
perimeter, even though they did not tell you all of the sides.
Example 2: A square has a side measuring 12 meters. What is the perimeter of
this square? (Draw a picture)
Example 3: Find the perimeter of the given right triangle.
7cm
5cm
3cm
9cm
6cm
3ft
5ft
4
* And sometimes, you might be given the perimeter and asked to find a missing
piece of the picture.
Example 4: If the perimeter of the following diagram is 45 in, find the missing side.
Example 5: If a rectangle has a perimeter of 30ft and the length of the rectangle
is 10ft, what is the width? (Draw a picture)
Example 6: The perimeter of this isosceles trapezoid is 92. Find the value of x.
8in
6in
4in
x
12in
x+2
x x
x+10
5
Practice
1. If a rectangle has a length of 7 ft and a width of 9 ft, what is its perimeter?
2. Find the perimeter of a right triangle with legs that are of length 6 cm and
8 cm.
3. If the perimeter of the following polygon is 33 in, find the missing side.
4. The perimeter of a square is 100 m. What is the length of each side?
x
15 9
4
6
Name______________________________________ Date____________________
HW#1
1. Find the perimeter of the given right triangle.
2. If a rectangle has a perimeter of 72ft and the length of the rectangle is 15ft,
what is the width?
3. The perimeter of this triangle is 88. Find the value of x
4. A square has a side measuring 16 ft. What is the perimeter of this square?
Review
1. Factor:
x2 17x 30 _______________________
2. Solve for x:
x
3x 2
4 _______________________
3. Find the slope between the points (2, 3) and (-4, 1)?
8
15
2x - 3
7x 5x+7
7
Formulas for Area
Figure Formula Example
Square A =
Rectangle A =
Triangle A =
Parallelogram A =
Trapezoid A =
6cm
3m
m
5m
4ft
10ft
4in
7in
4
20
8
side s
length
width w
l
height
base b
h
h
b
height
base
height
base2
base1
h
b2
b1
8
Area of Rectangles and Squares
Area – ______________________________________________________________________.
Area is measured in _________________ __________, such as ______ or _______, etc.
Depending on the figure, we use the appropriate formula to calculate the area.
The only and best way to remember these formulas is to MEMORIZE them!!!
Find the area of the following figures:
Example 1: Rectangle Example 2: Square
Not all area questions will be straightforward in asking you to find the area. They
might go about it in another way.
Example 3: The perimeter of a square is 36 in. What is the area of this square?
(Draw a picture!)
Example 4: Find the area of the given rectangle.
6ft
8ft
11in
12cm
13cm
9
Sometimes you are given the area and asked to find a missing piece of the
diagram or shape.
Example 5: The area of rectangle MATH is 54 square units. If the length of the
rectangle is 9 units, what is the perimeter of rectangle MATH?
Hint: Draw a picture to see what is missing and solve for it!
Example 6: A square has an area of 81 ft2. What is the length of each side?
Practice
1. The perimeter of a rectangle is 48 m. What is the area of the rectangle if
the length is 4 m?
2. A square has area of 144 in2. What is the perimeter of the square?
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Name______________________________________ Date____________________
HW#2
1. Find the areas of the following figures.
a. b.
2. A square has an area of 225 cm2. What is the length of each side?
3. Find the perimeter and area of the given rectangle.
Challenge
1. The area of this rectangle is 360 units2. Find the value of y.
Review
1. What is 20% of 35? _______________________________
2. What is the slope of the line x = -2? _________________________
7in
12in
15
7m
25m
y + 1
20
11
My height is measured the
same as a triangle, straight
from top to bottom.
Area of Triangles
You cannot use the same formula for triangles that you used for rectangles and
squares. Let’s investigate what the formula should be.
This is a rectangle. What is the area formula?
Now let’s draw in a diagonal.
The triangles take up __________ of the
rectangle, so the area formula is:
Find the area of the given triangles.
Example 1: Example 2:
Example 3: A right triangle has a hypotenuse of 13cm and one leg is 5cm. Find
the area of the triangle. (Draw a picture)
10m
3m 6
15
12
Find the missing piece given the area and some information.
Example 4: The area of triangle ABC is 45 ft2. If the base is 10 ft, what is the
height of triangle ABC? Show work!
Practice:
1. Find the area of the following triangle.
2. A right triangle has a hypotenuse of 61cm and one leg is 60cm. Find the area
of the triangle. (Draw a picture)
3. The area of triangle ABC is 84ft2. If the base is 7 ft, what is the height of
triangle ABC? Show work!
22m
7m
13
Name______________________________________ Date____________________
HW#3
1. Find the area of the triangles.
a. b.
2. The area of BUG is 76 ft2. If the base is 4 ft, what is the height of BUG?
3. A right triangle has a hypotenuse of 15 and one leg is 9. Find the perimeter
and area of the triangle.
Challenge:
1. The area of this right triangle is 100 m2. Find the value of x.
Review
1. Factor:
9y4 z10 _________________________
2. Solve for x: 8(x – 2) = 96
7
22 7ft
5ft
10
x - 4
14
Area of Trapezoids
A trapezoid is a four-sided shape, the bases are parallel and the
other sides (legs) are not.
Trapezoid is the longest formula of all of them!
A =
Label the picture with the pieces of the formula.
Example 1: Find the area of the given trapezoid.
Example 2: Find the area of the given trapezoid.
When working with a trapezoid, the height may be measured anywhere
between the two bases. Also, beware of "extra" information.
What is not needed to find the area? ____________________
3
8
4
15
Area of Parallelograms
A parallelogram looks like a rectangle tipped over.
Area of a parallelogram A =
Example 3: Find the area of the parallelogram.
Example 4: The area of a parallelogram is 120cm2. If the height is 12 cm, what is
the length of the base? (Draw a picture)
Practice:
1. Find the area of the following shapes:
a. b.
b. d.
2.1cm
4.7cm
3m
8m
7
18
10
5
13
11cm
16
Name______________________________________ Date____________________
HW#4
1. Find the area of the given trapezoid.
2. Find the area of the parallelogram.
3. The area of a parallelogram is 108cm2. If the height is 9 cm, what is the length
of the base?
Review: Multiply the following using FOIL
1. (x + 1)(x – 8) = ____________________ 2. (2x – 7)(x – 3) = ___________________
3. (x + 4)(x + 4) = ____________________ 4. (3x + 4)2 = _______________________
Factor the following:
1. 81x16 2 ________________________ 2. 75x10x2 _______________
3. xy5xy30yx15 242 ________________________
7
9
5
14cm
16cm
17
Area of a Shaded Region
When there is a shape within a shape and there is a shaded
region we must:
a) ______________________________________________________________
b) ______________________________________________________________
c) ______________________________________________________________
d) ______________________________________________________________
Example 1: Find the area of the shaded region.
a) Find the area of the large rectangle.
b) Find the area of the small rectangle.
c) Subtract and label!
Example 2: Find the area of the shaded region.
a) Find the area of the _______________.
b) Find the area of the _______________.
c) Subtract and label!
9ft
5ft 3ft
5ft
3in
2in
8in
3in
18
Example 3: Find the area of the shaded region.
Practice:
12ft
13ft
5ft
12in 5in
10in
6in
20in
19
Chris was hired to paint the front of this house. What is the area that the owner
expects him to paint? (Note: the downstairs windows are the same size, and the
upstairs windows are the same size.)
If the owner is going to pay him $6.25 per square foot to paint the front of the
house, how much would Chris earn on this job?
20ft
14ft
6ft
4ft
1ft
2ft
2ft
3ft
2ft
16ft
7ft
10ft
20
Name________________________________ Date_______________
HW #5
Show all formulas and label your answers.
1. Find the area of the shaded region outside of the square, but within the
rectangle.
2. Find the area of the shaded region.
3. Find the area of the shaded region outside of the triangle, but within the
trapezoid.
4. Review: What percent of 10 is 6?
5in
11in
3in
4
7
13
4
6
12
10
21
Volume of a Rectangular Solid (a box)
Volume: ____________________________________________________________________.
Volume is a 3-dimensional measurement so there is 3 pieces to the formula.
V = lwh
We label volume in ______________ ____________, such as _______ or _______, etc.
Example 1: Find the volume of a box with the dimensions of 4cm, 5cm, and
10cm.
Example 2: The volume of the figure below is 90 ft3. Solve for x and find the
dimensions of the box.
Example 3: The volume of the figure below is 140 in3. Solve for x and find the
missing dimension of the box.
2x
5
x
(x+3)
4
5
22
Practice:
1. Find the volume of the box with the dimensions 12in, 10in, and 26in.
2. The volume of the figure below is 84 ft3. Solve for x and find the dimensions of
the box.
Review:
3. The area of a rectangle is 572 in 2 and the height of the rectangle is 26in.
What is the length of the base of the rectangle?
4. Find the area of the figure to the right.
3x
7
x
8
23
12
23
Name_________________________________ Date_________________
HW #6
1. Find the volume of a box with the dimensions of 14in, 12in, and 5in.
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2. The volumes of the box is 96 in3. Solve for x and find the dimensions of the
box.
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3. The area of the triangle is 45 ft2. Solve for x.
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4. The volume of the box is 112 km3. Solve for x and find the missing dimension.
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5. These triangles are similar. Solve for x using proportions.
3
2x
4x
(x + 3)
7
2
6
3 x
10
18
x