G-6.6 FLASHCARD Area of Similar Figures

Front

What is the ratio of the areas of two similar figures if the ratio of their corresponding sides is 4:7?

Back

The ratio of the areas is the square of the ratio of the sides. Therefore, (4/7)² = 16/49.

Front

If the area of a smaller rectangle is 54 ft² and the ratio of the areas of two similar rectangles is 1:4, what is the area of the larger rectangle?

Back

The area of the larger rectangle is 4 * 54 ft² = 216 ft².

Front

Define similar figures in geometry.

Back

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

Front

What is the formula to find the area of a rectangle?

Back

Area = length × width.

Front

If two similar pentagons have a side length ratio of 5:9, what is the ratio of their areas?

Back

The ratio of their areas is (5/9)² = 25/81.

Front

How do you find the ratio of the areas of two similar triangles?

Back

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Front

What is the area of a rectangle with a length of 12 ft and a width of 9 ft?

Back

Area = 12 ft × 9 ft = 108 ft².

Front

If the area of a larger figure is 108 ft² and the area of a smaller figure is 54 ft², what is the ratio of the areas?

Back

The ratio of the areas is 108:54, which simplifies to 2:1.

Front

What does it mean for two figures to be proportional?

Back

Two figures are proportional if their corresponding sides are in the same ratio.

Front

If the ratio of the areas of two similar figures is 49:16, what is the ratio of their corresponding sides?

Back

The ratio of their corresponding sides is the square root of the area ratio, which is √(49/16) = 7/4.