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Similar Figures and Scale Models

Total questions: 15

Worksheet time: 15mins

Name
Class
Date
1.

Sides in similar figures must be proportional.  

a)

True

b)

False 

2.

Find missing side

a)

5

b)

7

c)

9

d)

11

3.

On a map, the distance between two towns in 2.6 cm. The scale of the map is 1 cm:50 km. What is the actual distance between the two towns?

a)

100 km

b)

130 km

c)

70 km

d)

150 km

4.

A rectangular garden is 45 ft wide and 70 ft long. On a blueprint, the width is 9 in. Identify the length on the blueprint. 

a)

7 in

b)

9 in

c)

12 in

d)

14 in

5.

Find the height of the tree.

a)

8 ft

b)

12 ft

c)

13 ft

d)

15 ft

6.

The blueprint(drawing) of this house has a length of 6 inches.  The actual house has a length of 18 feet.  What is the scale used?

a)

1 inch: 3 feet

b)

1 inch: 6 feet

c)

3 inches: 6 feet

d)

3 inches: 12 feet

7.

Scale: 1in.=7ft. The actual width of the backyard is 49 ft, how wide is it in the drawing?

a)

14 in 

b)

7 in

c)

42 in

d)

56 in

8.

Two spheres have a scale factor ratio of 1:3.  The smaller sphere has a surface area of 16 ft2.  Find the surface area of the larger sphere.

a)

48 ft2

b)

144 ft2

c)

432 ft2

d)

32 ft2

9.

Two similar pyramids have heights of 4 inches and 7 inches.  What is the ratio of the volume of the small pyramid to the volume of the large pyramid? 

a)

4:7

b)

16:49

c)

64:343

d)

12:21

10.

The surface area of a rectangular prism is 166 square feet. A similar prism has a surface area of 1494 square feet. If the length of the smaller prism is 5 feet, what is the length of the larger prism?

a)

10

b)

15

c)

45

d)

50

11.

The two rectangles are similar. Which is the length of the longer side of the blue rectangle?

a)

161

b)

110

c)

132

d)

53

12.

This 2 triangles a similar. Which of the following proportions will allow us to find the missing side AC?

a)

43=AC12\frac{4}{3}=\frac{AC}{12}

b)

520=AC4\frac{5}{20}=\frac{AC}{4}

c)

4AC=123\frac{4}{AC}=\frac{12}{3}

d)

12AC=35\frac{12}{AC}=\frac{3}{5}

13.

The Sagrada Família is a very much visited church in Barcelona. A store is selling scale models of the church to tourists. The scale of the models is 2 inches to 31 yards. If the models are 12 inches high, how high is the real church?

a)

186 yards

b)

24 yards

c)

360 yards

d)

1,000 inches

14.

Quadrilateral PQRT is similar to UVWX. Which statement about this quadrilaterals must be true?

a)

PRQR=UXVW\frac{PR}{QR}=\frac{UX}{VW}

b)

Angle PQR is congruent with angle UVW

c)

PQRT=WXUV\frac{PQ}{RT}=\frac{WX}{UV}

d)

Angle TPQ is congruent with angle VWX

15.

Pentagon FGHJK is similar to pentagon MPQST. What is the value of x?

a)

13.5

b)

27

c)

24

d)

not here