Chapter 11.4, Problem 9ST1

To determine

To Find: The area of the polygon.

Answer to Problem 9ST1

  $A=5xy$

Explanation of Solution

Given: A regular decagon with side $x$ and apothem $y$.

Given: Apothem = $y$

Number of sides in decagon is $10$

Thus

Perimeter of the decagon.

  $\begin{array}{l}P=10s\\ P=10(x)\\ P=10x\end{array}$

Now

Area of decagon

  $\begin{array}{l}A=\frac{1}{2}ap\\ A=\frac{1}{2}(y)(10x)\\ A=5xy\end{array}$

Hence, $A=5xy$ .