Unit A Homework

Homework
Geometry & Probability
Unit A
Name
Date
Period
Lesson 1 - Area Review
Shape Words Formula
Rectangle
The area A of a rectangle is the product of the
length and the width w.
A = w
Parallelogram
The area A of a parallelogram is the product of
any base b and its height h.
Exercises
Find the area of each figure. Show your work.
A = bh
1. _________________ 2. _________________
3. _________________ 4. _________________
5. _________________ 6. _______ __________

Homework
Geometry & Probability
Unit A
Name
Date
Period
Lesson 2 – More Area Review
Shape Words Formula
Triangle
The area A of a triangle is half the product of any
base b and its height h.
A = bh
Trapezoid
The area A of a trapezoid is half the product of
the height h and the sum of the bases, b1 and b2.
Exercises
Find the area of each figure. Show your work.
A = h (b1 + b2)
1. _________________ 2. _________________
3. _________________ 4. _________________
5. _________________ 6. _________________

Homework
Name
Geometry & Probability
Date
Unit A
Period
Lesson 3- Circumference
center
The diameter, d, is
the distance across a
circle through its
center.
The circumference, C,
is the distance around a
circle
The radius, r, is the
distance from the
center to any point
on a circle.
The diameter of a circle is twice its radius.
d = 2r
The radius is half the diameter. r =
The circumference of a circle is equal to
π times its diameter or π times twice its radius.
Examples
The radius of a circle is 7 meters. Find the
diameter.
Write the formula. d = 2r
Replace r with 7 d = 2 • 7
Multiply d = 14
The diameter is 14 meters.
7 m
C = πd
C = 2πr
Find the circumference of a circle with a radius
that is 13 inches. Use 3.14 for π. Round to the
nearest tenth.
Write the formula.
C = 2πr
Replace r with 13 and π with 3.14. C ≈ 2 • 3.14 • 13
Multiply. C ≈ 81.64
Rounded to the nearest tenth, the circumference
is about 81.6 inches.
Exercises
Find the circumference of each circle. Use 3.14 for π. Round to the nearest tenth if necessary.
Show your work.
1. _________________ 2. _________________ 3. _________________
5 m
8 in. 21 ft

Homework
Name
Geometry & Probability
Date
Unit A
Period
Lesson 4 - Area of Circles
The area A of a circle equals the product of pi (π) and the square of its radius r. A = πr 2
The formula for the area of a semicircle, or half a circle, is A = πr 2 .
Examples
Find the area of the circle.
Use 3.14 for π.
5 cm
Find the area of a semicircle that has a diameter of
9.4 millimeters. Use 3.14 for π. Round to the
nearest tenth.
A = πr 2
Area of semicircle
Area of circle A = πr 2
Replace π with 3.14 and r with 5. A ≈ 3.14 • 5 2
5 2 = 5 · 5 = 25 A ≈ 3.14 • 25
A ≈ 78.5
The area of the circle is approximately 78.5
square centimeters.
A ≈ • 3.14 • 4.7 2 Replace π with 3.14 and
A ≈ 34.7
r with 9.4 ÷ 2 or 4.7.
Multiply.
The area of the semicircle is approximately 34.7
square millimeters.
Exercises
Find the area of each circle. Round to the nearest tenth. Use 3.14 for π. Show your work.
1. _________________ 2. _________________ 3. _________________
7 in
25 mm
12 ft
Find the area of each semicircle. Round to the nearest tenth. Use 3.14 π. Show your work.
4. _________________ 5. _________________ 6. _________________
28 m
3 ft
GARDENING Vidur needs to buy
mulch for the garden with the
dimensions shown in the figure. For
how much area does Vidur need to
buy mulch?
5.5 yd

Homework
Geometry & Probability
Unit A
Name
Date
Period
Extended Constructed Response Question 3 2 1 0
Show your work & explain your answer.
John is scuba diving in the ocean. He begins at a depth of -232
feet. He swims down 87 feet to check out a shipwreck, and then
back up 101 feet when he sees a sting ray.
1. What is his current depth?
2. Draw a number line and record the three depths he hits. For example, you
would place a dot at -232 and label this “starting depth.” You must place his
depth after he swims down, and after he swims back up. (there will be three dots on your number line).
3. If 1 ft = 12 in, how many inches under water was John when he started? Explain your answer.
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Homework
Geometry & Probability
Unit A
Name
Date
Period
Lesson 5- Area of Composite Figures
To find the area of a composite figure, decompose the figure into shapes whose areas you know how
to find. Then find the sum of these areas.
Example
Find the area of the composite figure.
The figure can be separated into a semicircle and trapezoid.
Then, add the areas together.
The area of the figure is about 77.0 + 160 or 237 square inches.
Area of semicircle
Area of trapezoid
14 in.
10 in.
18 in.
14 in.
A = πr 2
A = h(b1 + b2 )
10 in.
A = • π • (7) 2
A ≈ 77.0 in 2
14 in.
A = • 10 • (14 + 18)
A = 160 in 2
18 in.
Exercises
Find the area of each figure. Round to the nearest tenth if necessary. Use 3.14 for π. Show your work.
1. _________________ 2. _________________ 3. _________________
8 mm
5 mm
6 mm
6 ft
9 ft
7 mi
14 mi
5 mi
5 mi
9 ft
4. _________________
SWIMMING POOLS The Cruz family is buying a custom-made cover for their swimming pool, shown below.
The cover costs $2.95 per square foot. How much will the cover cost? Round to the nearest cent.
15 ft
25 ft

Homework
Geometry & Probability
Unit A
Name
Date
Period
Lesson 6 - Volume of Prisms
The volume of a three-dimensional shape is the measure of space
occupied by it. It is measured in cubic units such of the shape at the right
can be shown using cubes.
The bottom layer,
or base, has 4 • 3
or 12 cubes.
→
There are
two layers.
It takes 12 • 2 or 24 cubes to fill the box. So, the volume of the box is 24 cubic meters.
A rectangular prism is a three-dimensional shape that has two parallel and congruent sides, or
bases, that are rectangles. To find the volume of a rectangular prism, multiply the area of the base
times the height, or find the product of the length , the width w, and the height h.
V = Bh or V = wh
Example
Find the volume of the rectangular prism
V = wh
Volume of a rectangular prism
V = 5 • 6 • 8 Replace with 5, w with 6, and h with 8.
V = 240
Multiply.
The volume is 240 cubic inches.
Exercises
Find the volume of each prism. Round to the nearest tenth. Show your work.
1. _________________ 2. _________________ 3. _________________
STICKY NOTES A triangular box
of sticky notes is shown. Find the
volume of the box.

ANSWERS:
Homework
Geometry & Probability
Unit A
Name
Date
Period
Mid-Unit Test Review
Calculate the correct answer to each problem. When finished, check your answers.
Exercises
Use 3.14 for π. Round to the nearest tenth. Show your work.
1. _______ What is the circumference of the circle?
A. 31. 2 yd C. 88.2 yd
B. 44.1 yd D. 176.5 yd
28.1 yd
2. _______ What is the area of the circle?
A. 1,017.4 mm 2 C. 56.5 mm 2
B. 254.3 mm 2 D. 28.3 mm 2
9 mm
3. _______ A rectangular trunk has a volume of 26,880 cubic inches. The trunk is 4
feet long by 28 inches wide. What is the trunk's height?
A. 20 in. C. 240 in.
B. 60 in. D. 2,880 in.
4. _______ What is volume of the right triangular prism?
A. 93.3m 3 C. 280 m 3
B. 140.3 m 3 D. 560 m 3
4 m 10 m 14 m
5. _________________ What is the area of the figure?
1C, 2B, 3C, 4C, 5 -1156.7 cm 2
18 cm
36 cm

Homework
Geometry & Probability
Unit A
Name
Date
Period
Extended Constructed Response Question 3 2 1 0
Show your work & explain your answer.
Bart, Lisa and Maggie Simpson order pizza for dinner to share.
Bart eats of a pizza, Lisa eats of a pizza and Maggie
eats
of a pizza.
1. Put the Simpsons in order from who eats the most pizza to who eats the least amount.
2. Create two equivalent fractions for the pizza Maggie ate. Draw a picture to show they are equivalent.
3. Is there any pizza left for Homer? If so, how much?
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Homework
Name
Geometry & Probability
Date
Unit A
Period
Lesson 7 - Comparing Volume Lab
Cylinder
Volume = πr 2 h
Surface Area = 2πrh + 2πr 2
h
r
Cone
Volume = πr 2 h
Exercises
Find the volume of each shape. Round to the nearest tenth. Use 3.14 for π. Show your work.
1. _________________ 2. _________________
10 in
3 in
3. The track-and-field club is planning a frozen yogurt sale to raise money. They need to buy containers to
hold the yogurt. They must choose between the cup and the cone below. Each container costs the same.
The club plans to charge customers $1.25 for a serving of yogurt. Which container should the club buy?
Why?
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Homework
Geometry & Probability
Unit A
Name
Date
Period
Lesson 8 - Volume of Pyramids
A pyramid is a three-dimensional shape with one base and triangular lateral faces.
The volume V of a pyramid is one third the area of the base B times the height h.
V = Bh
Examples
Find the volume of the pyramid.
Round to the nearest tenth.
V = Bh
Volume of a pyramid
11 m
V = ( w)h The base is a rectangle, so B = w.
4.3 m
3.2 m
V = (4.3 · 3.2) · 11 = 4.3, w = 3.2, h = 11
V ≈ 50.5
Simplify.
The volume is about 50.5 cubic meters.
Exercises
Find the volume of each shape. Round to the nearest tenth. Show your work.
1. _________________ 2. _________________ 3. _________________
6 cm
10 in.
7 in.
10 in.
8 cm
7 cm
13 in. 16 in.
2.3 in.
4. _________________
GATE POST The top of a gate post is in the shape of a square pyramid. The height of the pyramid is 5
inches and each side of the base is 7.4 inches. Find the volume of wood needed . to make the top of the
gate post

Homework
Geometry & Probability
Unit A
Name
Date
Period
Extended Constructed Response Question 3 2 1 0
Show your work & explain your answer.
Use your reference sheet.
The can of soup below has a radius of 4 cm and a height of 12 cm
1. What is the volume of the soup can?
2. Jeremy eats 65% of the soup for lunch. How much soup did he eat?
3. If Jeremy wants to pour the soup in the can into a Rubbermaid container (a square
prism) that has a side length of 6 cm and a height of 10 cm, how much space will be
left in the container??
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Homework
Geometry & Probability
Unit A
Name
Date
Period
Lesson 9 - Nets of 3-D Figures Lab
A net is a 2-D pattern for a 3-D shape.
Exercises
Can the pattern be folded along the lines to form a closed rectangular box? Explain for each pattern.
1. YES NO _______________________ 2. YES NO _______________________
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3. YES NO _______________________ 4. YES NO _______________________
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5. YES NO _______________________ 6. YES NO _______________________
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Homework
Geometry & Probability
Unit A
Name
Date
Period
Lesson 10 – Surface Area of Prisms
The sum of the areas of all the surfaces, or faces, of a three-dimensional shape is the surface area. The
surface area S.A. of a rectangular prism with length , width w, and height h is the sum of the areas of its
faces. S.A. = 2 w + 2 h + 2wh
Examples
Find the surface area of the rectangular prism. Faces Area
3 cm
4 m
3 cm
3 m
7 cm
2 m
2 m
4.9 ft
top and bottom 2 (4 · 3) = 24
front and back 2 (4 · 2) = 16
two sides 2 (2 · 3) = 12
sum of the areas 24 + 16 + 12 = 52
Alternatively, replace with 4, w with 3,
and h with 2 in the formula for surface area.
S. A. = 2 w + 2 h + 2wh
= 2 (4 · 3) + 2 (4 · 2) + 2 (3 · 2)
= 24 + 16 + 12
= 52
So, the surface area of the rectangular prism is 52 square meters.
4 m
back
4 m
2 m
side bottom side
2 m
3 m
front
top
3 m
Exercises
Find the surface area of each prism. Show your work.
1. _________________ 2. _________________ 3. _________________
3 ft
0.7 ft
8 mm
15 mm
17 mm
9 mm
4. _________________
CONTAINERS A company needs to package hazardous chemicals in special plastic rectangular prism
containers that hold 80 cubic feet. Find the whole number dimensions of the container that would use the
least amount of plastic.

Homework
Name
Geometry & Probability
Date
Unit A
Period
Lesson 11 – Relating Surface Area and Volume Lab
Surface Area of a Rectangular Prism = 2 w + 2 h + 2wh
Volume of a Rectangular Prism = wh
To find the surface area of a triangular prism, it is more efficient
to find the area of each face and calculate the sum of all the
faces rather than use a formula
Exercises
Each of these boxes holds 36 ping-pong balls.
Volume of a Prism = Bh
Box D
Box A
Box B
Box C
1. Without figuring, which box has the least surface area? Explain.
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Find the surface area of each box. Show your work.
2. ______________ 3. ______________ 4. ______________ 5. ______________
6. Draw a sketch of a triangular prism with a
volume of 120 cubic units and a surface area
of 184 square units. Label the dimensions.
HINT: The triangle is an isosceles triangle
with two sides with a length of 5 units.

ANSWERS:
1B, 2B, 3C, 4C, 5-14 in
Homework
Geometry & Probability
Unit A
Name
Date
Period
Mid-Unit Test Review
Calculate the correct answer to each problem. When finished, check your answers.
Exercises Show your work. Round to the nearest tenth, if necessary.
1. _______ What is the volume of the pyramid?
A. 32 in 3 C. 72 in 3
B. 48 in 3 D. 144 in 3
6 in.
4 in.
6 in.
2. _______ What is the volume of the pyramid?
A. 2,352 m 3 C. 1,176 m 3
B. 392 m 3 D. 261.3 m 3
7 m
24 m
14 m
25 m
3. _______ What is the surface area of the figure?
A. 185 m 2 C. 370 m 2
B. 231 m 2 D. 462 m 2
6 m
4. _______ What is volume of the right triangular prism?
A. 134 ft 2 C. 288 ft 2
B. 144 ft 2 D. 336 ft 2
11 m
12 ft
6 ft
8 ft
10 ft
7 m
5. _________________ A drawer is shaped like a rectangular prism. It has a length
of 17 inches and a height of 6 inches. The volume is 1,428 cubic inches. Find the
width of the drawer.
Remember: your test will include all the lessons from the start of the unit. Go back over all previous materials.

Homework
Geometry & Probability
Unit A
Name
Date
Period
Extended Constructed Response Question 3 2 1 0
Show your work & explain your answer.
A company will make a cereal box with whole number
dimensions and a volume of 100 cubic centimeters.
1. Make a list of all the possible box dimensions.
2. If cardboard costs $0.05 per 100 square centimeters, what is
the least cost to make 100 boxes? Explain.
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Homework
Geometry & Probability
Unit A
Name
Date
Period
Lesson 12 – Surface Area of Pyramids
The total surface area S.A. of a regular pyramid is the
lateral area L.A. plus the area of the base.
S.A. = B + L.A. or S.A. = B + P
Examples
Find the total surface area of the pyramid.
6 in.
Find the total surface area of the pyramid.
5 m
Perimeter
of base P
Slant
height
Area of
base B
Surface area of a pyramid
S.A. = B +
P
7 in.
7 in.
S.A. = 49 + (28 ∙ 6) P = 4(7)= 28, = 6, B = 7 · 7= 49
S.A. = 133
Simplify.
The surface area of the pyramid is 133 square
inches.
6 m 6 m
6 m
S.A. = 15.6 + (18 ∙ 5) P = 3(6)= 18, = 5, B = 15.6
S.A. = 60.6
area of base
15.6 m 2
Simplify.
The surface area of the pyramid is 60.6 square
meters.
Exercises
Find the total surface area of each pyramid. Round to the nearest tenth. Show your work.
1. _________________ 2. _________________ 3. _________________
2 ft
3 ft
2 ft
TENT The Summers children are
camping out in the tent shown.
7 cm
Find the lateral area of the tent.
4 cm
9 ft.
4 cm 4 cm
area of base
6.9 cm 2
12 ft.
12 ft.

Homework
Geometry & Probability
Unit A
Name
Date
Period
Lesson 13-Volume of Composite Figures
Find the volume of each shape, then add together.
Example
The figure is made up of a rectangular prisms.
V = lwh + lwh
V = 2 • 1 • 1 + 2 • 0.5 • 0.5
V = 2 + 0.5
The volume of the composite figure is 2.5 cubic meters.
Exercises
Find the volume of the composite figure. Show your work.
1. _________________ 2. _________________ 3. _________________
6 ft
10 ft
4 in
20 ft
10 ft
4 in
8 in
10 in
4. Draw an example of a composite figure that has a volume between 250 and 300 cubic units.

Homework
Geometry & Probability
Unit A
Name
Date
Period
Lesson 14- Surface Area of Composite Figures
The circle, is A = πr 2 .
Example
To find the surface area, find the area of exposed surfaces.
The lateral area of the prism is 50 + 10 + 50 + 10 = 120 m 2 .
The area of the bottom of the prism is 10 × 2 = 20 m 2 .
The surface area of the triangular prism is 2 + 2 + 28 + 20 = 52 m 2 .
So, the surface area is 120 + 20 + 52 = 192 m 2 .
Exercises
Find the surface area of each figure. Show your work.
1. _________________ 2. _________________ 3. _________________
10 m
6 m
16 m
4 m
5 m
4. _________________
FLOWER BOX Find the surface area of the open-top flower box shown.

Homework
Geometry & Probability
Unit A
Name
Date
Period
Extended Constructed Response Question 3 2 1 0
Show your work & explain your answer.
Look at the following expression.
117 – 3(4 + 2) 2 + 6
Part A
What are the first two steps you would take to find the value of this expression?
Explain.
Part B
Find the value of the expression. Be sure to rewrite the expression after each step.
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