Area Adventures: Comparing Similar Figures in Geometry

1. A rectangle has a length of 8 cm and a width of 4 cm. If a similar rectangle has a length of 12 cm, what is its width?

• 6 cm

• 7 cm

• 5 cm

• 9 cm

2. Two triangles are similar. The first triangle has an area of 20 square cm, and its corresponding side is 5 cm. If the corresponding side of the second triangle is 10 cm, what is the area of the second triangle?

• 60 square cm

• 100 square cm

• 80 square cm

• 40 square cm

3. A small park is shaped like a square with sides of 10 m. A larger similar park has sides of 15 m. How much larger is the area of the larger park compared to the smaller park?

• 125 m²

• 75 m²

• 100 m²

• 150 m²

4. A model of a building is similar to the actual building. If the model has a height of 2 m and the actual building is 10 m tall, what is the ratio of their heights?

• 2:5

• 1:5

• 1:2

• 1:10

5. A triangle has a base of 6 cm and a height of 4 cm. If a similar triangle has a base of 9 cm, what is the height of the similar triangle?

• 7 cm

• 6 cm

• 5 cm

• 8 cm

6. Two similar rectangles have areas of 50 square meters and 200 square meters. What is the ratio of the lengths of their corresponding sides?

• 3:4

• 2:3

• 1:3

• 1:2

7. A small painting is similar to a larger painting. If the small painting has an area of 30 square inches and the larger painting has a side length that is twice as long, what is the area of the larger painting?

• 120 square inches

• 150 square inches

• 90 square inches

• 60 square inches

8. A square garden has an area of 64 square feet. If a similar garden has a side length that is 1.5 times longer, what is the area of the larger garden?

• 96 square feet

• 144 square feet

• 100 square feet

• 128 square feet

9. A smaller similar trapezoid has an area of 15 square cm. If the ratio of the sides of the larger trapezoid to the smaller one is 3:1, what is the area of the larger trapezoid?

• 60 square cm

• 45 square cm

• 90 square cm

• 135 square cm

10. Two similar circles have radii of 4 cm and 6 cm. What is the ratio of their areas?

• 2:3

• 1:2

• 4:9

• 5:8