Unit Study Guide - Geometry - ANSWER KEY

[Pages:4]Unit Study Guide Geometry ANSWER KEY

Which line segment's length can be calculated by using the expression 52?

A. BC

B. DA

C. DC

D. AB The distance between B and C is the difference of 5 and 2.

B

C

A

D

Answer:____A____

#1

What is the surface area of the cube shown

below?

Since it is a cube. Find the area

of one side and multiply by 6.

1/2 in.

A = L x W

A = 1/2 x 1/2 = 1/4in2

SA = 1/4 x 6

1 4

2

x

613=

3 2

= 1 1/2 in2

Answer:_1__1_/2_in_2__

#2

A water tank is filled with 136 cubic inches of

water. How much water is needed to fill the rest

of the tank?

V = L x W X H

V = 12.2 x 5 x 8

8 in.

V = 488 in3

5 in.

Steps: 12.2 in.

Find the total volume.

Subtract the total volume and what is already in the tank.

488 Total Area 136 Water in tank 352 Water needed

Answer:_3_5_2__in_3__

#3

What is the area of a figure with vertices at ( 3 , 4 ), ( 2 , 4 ), (5 , 1 ) and ( 4 , 1)?

3

3

25 2

A= bh 2

A= (2)(3)

2

A = 3 u2

A = L x W

A = 3 x 5 A = 15 u2

Total Area = 3 + 15 + 3

Total Area = 21 units2

Answer:_2_1_u_n_i_ts_2_

#4

8 units 8 units 20 cm.

What is the perimeter of a figure that has

vertices at points ( 3 , 3 ), ( 3 , 3), ( 3 , 5 ), and

( 3, 5)?

6 units

8 units 8 units

6 units 6 units

6 units P = 6 + 8 + 6 + 8 P = 28 units

Answer:_2_8__u_n_it_s_

#5

Find

the

area

of

the

shaded

region.

Area of Shaded Region would be

30 cm.

the area of the

rectangle minus

4 cm.

the sum of the

3 cm.

triangle and the

5 cm.

parallelogram

6 cm.

600 Total 27 Unshaded

Triangle Parallelogram Rectangle 573 Shaded

A = bh/2 A = (5)(6)/2 A = 15cm2

A = bh A = (3)(4) A = 12cm2

Area = L x W

Area = 20 x 30 Area = 600cm2

15 + 12 = 27cm2 (Unshaded Area)

Answer:_5_7_3__c_m_2_

#6

1

Unit Study Guide Geometry ANSWER KEY

The net below is a representation of what figure?

A. Rectangular pyramid B. Triangular prism C. Rectangular prism D. Rectangle

Answer:____B____

#7

The base of the triangle is three times the height. What is the area of the triangle?

4 1/3 ft.

13 ft.

Steps: Since the base is three times the height multiply 4 1/3 by 3 to find the base. Then use the area of a triangle formula to solve it.

4 1/3 x 3

13 3

x3 1

= 13

A = bh 2

A = (13)(4 1/3) 2

A = 28 1/6 ft2

Answer:__2_8_1_/6_f_t2_

#8

David's backyard is shaped like the one below.

A = 16ft2

4 ft.

6 ft.

A = 36ft2

?

5.5 ft.

If the area is 155.5 feet squared, what is the

length of side for the rectangle? 11.5 103.5

Steps:

Subtract the area of the two squares from the total area.

Take the remaining area and divide by the side (11.5).

155.5 52.0 103.5

0009 115 1035.

1035

0

Answer:___9_f_t ___

#9

11.5 ft 8 units

8 units

What is the area of a triangle with vertices at ( 3 , 6 ), ( 3 , 2 ), and ( 3 , 2)?

6 units

6 units A = bh

2 A = (8)(6)= 48 = 24

22

Answer:_2_4__u_n_its_2_

#10

Greg is putting a new cover on one of his couch cushions. The cushion is in the shape of a rectangular prism. Greg drew a net of the cushion below. What is the minimum amount of fabric Greg needs to cover the cushion?

3 x 101/2=31 1/2in2

10 1/2 in.

7 x 3 = 21in2

7 x 3 = 21in2

7 in.

7 x 10 1/2= 73 1/2in2

3 in. 3 x 101/2=31 1/2in2

Find the area of each rectangle. Then add them all up.

31 1/2 + 31 1/2 + 73 1/2 + 73 1/2 + 21 + 21=

7 x 10 1/2=

252 in2

73 1/2in2

Answer:__2_5_2_i_n_2 _

#11

What is the area of the figure on the coordinate

plane?

Break into triangles

and find the area of

each triangle.

A = bh = (4)(2) = 4 22

Each triangle is 4u2. You have two triangles that are the same so 4 x 2 is 8 units squared.

Answer:_8__u_n_it_s_2 _

#12

2

Unit Study Guide Geometry ANSWER KEY

Find the area of the shaded region.

Section off the figure

into shapes you know.

Find the area of each

and add them together.

Triangle

A = bh/2 A = (4)(4)/2 = 8u2

Total Area = 8 + 24 + 9 = 41u2

Rectangle A = l x w A = 6 x 4 = 24u2

Trapazoid A = 1/2h(b1 + b2) A = 1/2(3)(2 + 4) A = 9u2

Answer:___4_1u_2___

#13

A roll of carpet will cover 42 1/2 square feet.

What length of a 8 1/2 foot wide room can one

roll cover?

A=L W

42 1/2 = 8 1/2 W

8 1/2

8 1/2

42 1/2 8 1/2 = W

85 2

17 2

= W

58K5 2

1

C F 21 = W 171

5 = W

Answer:__5_f_e_e_t __

#14

What is the surface area of the triangular pyramid below? The base triangle is an equilateral triangle with a perimeter of 36 inches.

55.2in2 55.2in2

7 in.

55.2in2 42in2

9.2 in. If the perimeter is 36 then the base has to be 12 for each. SA = 55.2 + 55.2 + 55.2 + 42

SA = 207.6in2

Inside Triangle

A = bh/2 A = (12)(7)/2 = 42in2

3 Outside Triangles

A = bh/2 A = (12)(9.2)/2 = 55.2in2

Answer:__2_07_._6_in_2 _

#15

Steven is packing a box with cubes. The box

has a length of 2/3 foot (ft), a width of 1 ft and a height of 3/4 ft. How many cubes with an edge length of 1/4 ft will it take to fill the box? Step #1 Volume of Prism Step #3

V = L x W x H V = 2/3 x 1 x 3/4 V = 1/2 ft3

Step #2Volume of the Cube

V = L x W x H V = 1/4 x 1/4 x 1/4 V = 1/64 ft3

1 2

1 64

=

K C F

1 2

64 1

=

64 2

=32

32 cubes

Answer:_3_2_c_u_b_e_s_

#16

What is the area of the figure below. Find the area of one

6.2 in.

triangle and multiply it by 6.

4 in.

A = bh = (6.2)(4) = 24.8 = 12.4

2

2

2

12.4 x 6 = 74.4 in2

Answer:__7_4_.4__in_2_

#17

Draw and label a net for a triangular pyramid

with four equilateral triangles. The base of the

triangles is 15 cm., and the height is 9.4 cm.

What is the surface area of the pyramid?

Find the area of 1 triangle then multiply it

by 4 since they are all the same.

A = bh = (15)(9.4) = 141 = 70.5cm2

2

2

2

15cm

70.5 x 4 = 282 cm2

9.4cm 15cm

15cm

Answer:_2_8_2__c_m_2_

#18

3

Unit Study Guide Geometry ANSWER KEY

What is the surface area of the rectangular

prism below?

1/3 ft.

1/2 ft.

3 ft.

Front/Back A = L x W

A = (1/2)(1/3)

A = 1/6 ft2

Find the area of each side then add all 6 of them up.

Sides

Top/Bottom

A=LxW A=LxW

A = (3)(1/3) A = (1/2)(3) A = 1 ft2 A = 1 1/2 ft2

SA = 1/6 + 1/6 + 1 + 1 + 11/2 + 11/2 = 5 2/6 = 5 1/3ft2

Answer:__5_1_/3_ft_2 __

#19

The points ( 4 , 1 ), ( 1, 1 ) and ( 4 , 3 ) are three vertices of a rectangle. What are the coordinates of the fourth vertex of the rectangle? A. ( 1 , 4 ) B. ( 3 , 1 ) C. ( 4 , 1 ) D. ( 1 , 3 )

Answer:___D_____

#20

Find the volume of the rectangular prism.

6m

V = L x W x H

V = 10 x 4 x 6

4m 10m

V = 240 m3

Answer:__2_4_0_m__3 _

#21

The figure below is a cube. The base area is 81

square inches. Find the total volume of the

cube.

Since you know it is a cube

all measurements are the

same. If you have the base

are you have to ask

yourself what number

times itself gives you 81.

The answer is 9. Now you

can find the volume. V = L x W x H

V = 9 x 9 x 9 = 729 in3

Answer:__7_2_9_i_n_3 _

#22

A storage box is shaped like a rectangular

prism, as shown below. Zac stored 1/2 inch

cubes in the box. How many cubes are needed

to completely fill the box?

Step 2: Volume of the cube

1 1/2 in

V = L x W X H V = 1/2 x 1/2 X 1/2

2 in

V = 1/8 in3 Step 3: Divide them

4 in

Step 1: Vol of the Box V = L x W X H

12 1/8 12 1 18

V = 4 x 2 X 1 1/2

K C F

V = 12 in3

12 1

x

8 1

=

96

cubes

Answer: _9_6_c_u_b_e_s_

#23

Tony has a vase in the shape of a rectangular

prism that he plans to fill with blue and red

sand. The vase has a length of 5 cm, a width of

7 cm, and a height of 9 cm. If the vase already

has 207 1/3 cm of blue sand. How much red sand can he pour to completely fill the vase.

Volume of Vase V = L x W x H

Red Sand would be Total Sand Blue Sand

V = 5 x 7 x 9 V = 315 cm3

315 207 1/3 = 314 3/3 207 1/3 = 107 2/3

Blue Sand

107 2/3 cm3 of red sand

207 1/3 cm3

Answer:1_0_7__2_/3_c_m_3

#24

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