Chapter 11.5, Problem 29HP

To determine

To Find: The way to find the area of the enlarged polygon if you know the area of the original polygon and the scale factor of the enlargement.

Answer to Problem 29HP

The expression for the area of the enlarged polygon is $A_{enlarged}=A_{original}{k}^2$

Explanation of Solution

Calculation:

Consider the area of the original polygon is $A_{original}$ and the scale factor is k.

Then, by the theorem of the similar polygon, the area of the enlarged figure is obtained as,

  $\begin{array}{l}{k}^2=\frac{A_{enlarged}}{A_{original}}\\ A_{enlarged}=A_{original}{k}^2\end{array}$