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Similar figures
This test applies the properties of similar figures and the scale factor. Tasks involve corresponding sides, perimeters and areas and develop understanding that areas change by the square of the scale factor.
Questions: 10Estimated time: 18 minutes
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Question 1out of 10
Corresponding sides of similar figures are 3 cm and 9 cm. Find the scale factor.
Similar figures have equal corresponding angles and proportional sides. Lengths and perimeters scale by k; areas by k². Find k as target length divided by original length. Multiply area by k² to enlarge and divide to shrink. Sides 4 and 12 give k = 3 and an area factor of 9.
Question 2out of 10
Similar figures have perimeters 40 cm and 80 cm. What is the ratio of the larger area to the smaller area?
Similar figures have equal corresponding angles and proportional sides. Lengths and perimeters scale by k; areas by k². Find k as target length divided by original length. Multiply area by k² to enlarge and divide to shrink. Sides 4 and 12 give k = 3 and an area factor of 9.
Question 3out of 10
The larger area is 99 cm² and the area ratio is 9. Find the smaller area.
Similar figures have equal corresponding angles and proportional sides. Lengths and perimeters scale by k; areas by k². Find k as target length divided by original length. Multiply area by k² to enlarge and divide to shrink. Sides 4 and 12 give k = 3 and an area factor of 9.
Question 4out of 10
In similar triangles, 10 cm corresponds to 20 cm, while 7 cm corresponds to X. Find X.
Similar figures have equal corresponding angles and proportional sides. Lengths and perimeters scale by k; areas by k². Find k as target length divided by original length. Multiply area by k² to enlarge and divide to shrink. Sides 4 and 12 give k = 3 and an area factor of 9.
Question 5out of 10
Which statement describes similar figures?
Similar figures have equal corresponding angles and proportional sides. Lengths and perimeters scale by k; areas by k². Find k as target length divided by original length. Multiply area by k² to enlarge and divide to shrink. Sides 4 and 12 give k = 3 and an area factor of 9.
Question 6out of 10
The larger area is 128 cm² and the area ratio is 16. Find the smaller area.
Similar figures have equal corresponding angles and proportional sides. Lengths and perimeters scale by k; areas by k². Find k as target length divided by original length. Multiply area by k² to enlarge and divide to shrink. Sides 4 and 12 give k = 3 and an area factor of 9.
Question 7out of 10
A figure has area 70 cm². The scale factor to a larger figure is 5. Find its area.
Similar figures have equal corresponding angles and proportional sides. Lengths and perimeters scale by k; areas by k². Find k as target length divided by original length. Multiply area by k² to enlarge and divide to shrink. Sides 4 and 12 give k = 3 and an area factor of 9.
Question 8out of 10
The corresponding sides of two similar figures are 2 cm and 4 cm. Compare their areas.
Similar figures have equal corresponding angles and proportional sides. Lengths and perimeters scale by k; areas by k². Find k as target length divided by original length. Multiply area by k² to enlarge and divide to shrink. Sides 4 and 12 give k = 3 and an area factor of 9.
Question 9out of 10
A figure has perimeter 28 cm. The scale factor to a larger figure is 2. Find its perimeter.
Similar figures have equal corresponding angles and proportional sides. Lengths and perimeters scale by k; areas by k². Find k as target length divided by original length. Multiply area by k² to enlarge and divide to shrink. Sides 4 and 12 give k = 3 and an area factor of 9.
Question 10out of 10
In similar triangles, 6 cm corresponds to 30 cm, while 10 cm corresponds to X. Find X.
Similar figures have equal corresponding angles and proportional sides. Lengths and perimeters scale by k; areas by k². Find k as target length divided by original length. Multiply area by k² to enlarge and divide to shrink. Sides 4 and 12 give k = 3 and an area factor of 9.
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Sample questions
- A figure has perimeter ___ cm. The scale factor to a larger figure is ___. Find its perimeter.
- A figure has area ___ cm². The scale factor to a larger figure is ___. Find its area.
- Corresponding sides of similar figures are ___ cm and ___ cm. Find the scale factor.
- The larger area is ___ cm² and the area ratio is ___. Find the smaller area.
- In similar triangles, ___ cm corresponds to ___ cm, while ___ cm corresponds to X. Find X.
Similar figures
Corresponding angles of similar figures are equal and corresponding sides are proportional. The scale factor k is the ratio of a new corresponding length to the original one.
Length, area and volume
Lengths scale by k, areas by k² and volumes of similar solids by k³. Match corresponding vertices and sides correctly and write every side ratio in the same direction. Triangle similarity can be established using equal angles or proportional sides.
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