Question

If the scale factor is 5, how many times larger will the scaled copy's area be?

Answer 1

25 times

Explanation:

Scale factor is the ratio of dimensions of the image and the preimage.

Scale factor =
`\frac{\text{Side length of image}}{\text{Side length of preimage}}`

Since area of a figure is the square of dimensions.

Area = Length × Width

Therefore, area scale factor will be the ratio of square of the dimensions of image and preimage.

Area scale factor =
`\frac{\text{Area of the image}}{\text{Area of the preimage}}`

= (Scale factor)²

= 5²

= 25

Therefore, area of the image will be 25 times the area of the preimage.