Area 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 the lengths of corresponding sides are proportional.

Front

How do you find the area of similar figures?

Back

To find the area of similar figures, use the ratio of the lengths of corresponding sides. If the ratio of the sides is a:b, then the ratio of the areas is a²:b².

Front

If two similar triangles have a side length ratio of 2:3, what is the ratio of their areas?

Back

The ratio of their areas is 2²:3², which simplifies to 4:9.

Front

Given two similar rectangles with a length ratio of 1:4, what is the area ratio?

Back

The area ratio is 1²:4², which simplifies to 1:16.

Front

What is the formula for the area of a rectangle?

Back

The area of a rectangle is calculated using the formula: Area = length × width.

Front

If the area of a smaller similar figure is 25 cm², what is the area of a larger figure if the side length ratio is 1:5?

Back

The area of the larger figure is 25 cm² × (5²) = 25 cm² × 25 = 625 cm².

Front

How do you determine the value of x in similar figures?

Back

To determine the value of x in similar figures, set up a proportion based on the lengths of corresponding sides and solve for x.

Front

If two similar figures have areas of 36 m² and 64 m², what is the ratio of their corresponding side lengths?

Back

The ratio of their corresponding side lengths is √(36):√(64), which simplifies to 6:8 or 3:4.

Front

What is the relationship between the perimeters of similar figures?

Back

The ratio of the perimeters of similar figures is the same as the ratio of their corresponding side lengths.

Front

If the side lengths of two similar figures are in the ratio 3:7, what is the ratio of their perimeters?

Back

The ratio of their perimeters is also 3:7.