Similar Figures (Area & Perimeter)

Front

What are similar figures?

Back

Similar figures are shapes that have the same shape but may differ in size. Their corresponding angles are equal, and the lengths of corresponding sides are proportional.

Front

How do you find the ratio of areas of similar figures?

Back

The ratio of the areas of similar figures is equal to the square of the ratio of their corresponding side lengths.

Front

If the ratio of the side lengths of two similar figures is 3:4, what is the ratio of their areas?

Back

The ratio of their areas is (3^2):(4^2) = 9:16.

Front

What is the formula for the perimeter of similar figures?

Back

The ratio of the perimeters of similar figures is equal to the ratio of their corresponding side lengths.

Front

If the perimeter of a larger figure is 24 cm and the ratio of the perimeters of two similar figures is 2:1, what is the perimeter of the smaller figure?

Back

The perimeter of the smaller figure is 24 cm / 2 = 12 cm.

Front

What is the relationship between the side lengths and the area of similar figures?

Back

If the ratio of the side lengths is a:b, then the ratio of the areas is a^2:b^2.

Front

How do you calculate the area of a rectangle?

Back

Area = length × width.

Front

If the area of a rectangle is 36 cm² and the length is 6 cm, what is the width?

Back

Width = Area / Length = 36 cm² / 6 cm = 6 cm.

Front

What is the formula for the area of a triangle?

Back

Area = 1/2 × base × height.

Front

If two triangles are similar and the ratio of their corresponding sides is 5:3, what is the ratio of their areas?

Back

The ratio of their areas is 5^2:3^2 = 25:9.