Question

A 20 sided regular polygon has a side length of 10 meters. What is the area of the polygon? Round to the nearest thousandth. Remember, you only need to draw a right triangle.

Answer 1

Divinding the polygon into right triangles, we have (20 x 2)= 40 right triangles in the polygon

Area of the polygon = 40 x Area of 1 right triangle inside

`\begin{gathered} \theta\text{ + }\theta=\text{ }(360)/(20) \\ 2\theta=18 \\ \theta=(18)/(2)=9^0 \end{gathered}`

From the triangle above,

`\begin{gathered} \tan \text{ }\theta=(5)/(h) \\ \tan \text{ 9 = }(5)/(h) \\ h=\frac{5}{\tan \text{ 9}} \\ h=31.57m \end{gathered}`

Area of the triangle = 1/2 x base x height

=1/2 x 5 x 31.57= 78.92 m^2

Area of the polygon = 40 x 78.92 m^2

=3156.8 m^2