Scale Factor Area and Length

Front

What is a scale factor?

Back

A scale factor is a number that scales, or multiplies, some quantity. It is used to determine how much larger or smaller a figure is compared to another figure.

Front

If the scale factor is 10, how does it affect the area of a shape?

Back

The area of the shape becomes 10^2 = 100 times larger.

Front

If a rectangle has an area of 40 cm² and is scaled by a factor of 10, what is the area of the new rectangle?

Back

The area of the new rectangle is 40 cm² x 100 = 4000 cm².

Front

What is the relationship between the scale factor and the area of similar shapes?

Back

The area of similar shapes is proportional to the square of the scale factor.

Front

If the side length of a square is doubled, how does the area change?

Back

The area becomes 2^2 = 4 times larger.

Front

What is the scale factor if the area of a larger square is 64 ft² and the area of a smaller square is 16 ft²?

Back

The scale factor is √(64/16) = √4 = 2.

Front

How do you find the actual distance using a map scale?

Back

Multiply the distance on the map by the scale factor to find the actual distance.

Front

If a map scale is 1 inch = 20 miles, how far is 5.5 inches on the map?

Back

5.5 inches x 20 miles/inch = 110 miles.

Front

What happens to the area of a shape if the scale factor is 1/2?

Back

The area becomes (1/2)^2 = 1/4 of the original area.

Front

If a rectangle's length is scaled by a factor of 3, how does the area change?

Back

The area becomes 3^2 = 9 times larger.