12.11 Area and Perimeter of Similar Figures

Front

What is the definition of similar figures?

Back

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

Front

How do you calculate the perimeter of similar figures?

Back

To find the perimeter of similar figures, use the ratio of their corresponding sides. If the scale factor is known, multiply the perimeter of the smaller figure by the scale factor to find the perimeter of the larger figure.

Front

What is the relationship between the areas of similar figures?

Back

The areas of similar figures are proportional to the square of the scale factor. If the scale factor is k, then the area ratio is k^2.

Front

If a triangle has a perimeter of 30 mm and is dilated by a scale factor of 2, what is the new perimeter?

Back

The new perimeter is 60 mm (30 mm x 2).

Front

What is the formula for the area of a rectangle?

Back

Area = length × width.

Front

If the length of a rectangle is doubled and the width remains the same, how does the area change?

Back

The area doubles because Area = length × width; if length is doubled, the new area is 2 × (length × width).

Front

What is the scale factor if the perimeter of a smaller triangle is 10.2 mm and the larger triangle is 23.8 mm?

Back

The scale factor is 2.33 (23.8 mm / 10.2 mm).

Front

How do you find the ratio of the perimeters of two similar figures?

Back

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

Front

If a figure is dilated by a scale factor of 4, what happens to its area?

Back

The area is multiplied by 16 (4^2).

Front

What is the perimeter of a triangle with sides measuring 3 mm, 4 mm, and 5 mm?

Back

The perimeter is 12 mm (3 mm + 4 mm + 5 mm).