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

Answer:

99 units²

Step-by-step 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,

$\text{Area}_{polygon}=\dfrac{1}{2}\cdot \text{Perimeter}\cdot \text{Apethom}$

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,

$=11\times 9$

$=99$ units²