Discovering Areas: Similar Figures in Action

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?

• 7 cm

• 6 cm

• 10 cm

• 5 cm

2. Two triangles are similar. The first triangle has a base of 6 cm and a height of 3 cm. If the second triangle has a base of 9 cm, what is its height?

• 6 cm

• 3 cm

• 4.5 cm

• 5 cm

3. A square has an area of 64 cm². If a similar square has a side length that is twice as long, what is the area of the larger square?

• 64 cm²

• 128 cm²

• 32 cm²

• 256 cm²

4. A model of a car is 1.5 m long and is similar to the actual car, which is 4.5 m long. If the model has an area of 3 m², what is the area of the actual car?

• 27 m²

• 9 m²

• 36 m²

• 15 m²

5. Two similar pentagons have a ratio of their sides of 2:3. If the area of the smaller pentagon is 20 cm², what is the area of the larger pentagon?

• 25 cm²

• 30 cm²

• 50 cm²

• 45 cm²

6. A smaller park is shaped like a rectangle with dimensions 10 m by 5 m. A similar larger park has a length of 15 m. What is the width of the larger park?

• 12 m

• 5 m

• 10 m

• 7.5 m

7. A triangle has an area of 30 cm². If a similar triangle has a height that is 1.5 times greater, what is the area of the larger triangle?

• 90 cm²

• 60 cm²

• 67.5 cm²

• 45 cm²

8. A smaller painting is 12 inches wide and 16 inches tall. If a similar larger painting has a width of 18 inches, what is its height?

• 20 inches

• 26 inches

• 24 inches

• 22 inches

9. Two similar circles have radii in the ratio of 1:4. If the area of the smaller circle is 12.56 cm², what is the area of the larger circle?

• 200.96 cm²

• 50.24 cm²

• 100.48 cm²

• 78.5 cm²

10. A rectangular garden is 10 m long and 6 m wide. If a similar garden is scaled up by a factor of 2, what will be the area of the larger garden?

• 60 m²

• 120 m²

• 180 m²

• 240 m²