Question

Polygon Y has an area of 11 square units. Celia drew a scaled version of Polygon Y using a scale factor of 3 and labeled it Polygon Z. What is the area of Polygon Z?

Answer 1

The ratio of the areas = the ratio of the squares of the scale factor.

So the area of Z is 3^2 * 11 = 99 sq units.

Answer 2

99 units²

Explanation:

Polygon Y has an area of 11 square units. i.e the area of original figure is 11 square units.

Celia drew a scaled version of Polygon Y using a scale factor of 3 and labeled it polygon Z.

So the original figure is expanded 3 times. So its sides and apothem will be 3 times of the previous length.

As we know that,

`\text{Area}_(polygon)=(1)/(2)\cdot \text{Perimeter}\cdot \text{Apethom}`

As along with the sides, the perimeter and apethom also increases 3 times. Hence, the area will increase 3×3 = 9 times.

Therefore, the area of the polygon Z will be,

`=11* 9`

`=99` units²