8.2.1 Geometry Ratio of Areas

Front

What is the ratio of the areas of two similar figures if the ratio of their corresponding sides is 4:1?

Back

The ratio of the areas is 4^2:1^2 = 16:1.

Front

If the area of a square is 64 square units, what is the length of one side?

Back

The length of one side is 8 units.

Front

What happens to the perimeter of a figure when it is dilated by a scale factor of k?

Back

The perimeter is multiplied by k.

Front

What happens to the area of a figure when it is dilated by a scale factor of k?

Back

The area is multiplied by k^2.

Front

If two triangles are similar, what is the relationship between their corresponding sides?

Back

The ratios of their corresponding sides are equal.

Front

If the ratio of the perimeters of two similar figures is 3:2, what is the ratio of their areas?

Back

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

Front

How do you find the missing side of a similar figure?

Back

Set up a proportion using the ratios of corresponding sides.

Front

What is the scale factor if the area of a figure is increased from 25 square units to 100 square units?

Back

The scale factor is 2 (since 100/25 = 4, and the square root of 4 is 2).

Front

If the ratio of the areas of two circles is 1:4, what is the ratio of their radii?

Back

The ratio of their radii is 1:2.

Front

What is the formula for the area of a triangle?

Back

Area = 1/2 * base * height.