Question

find the area of a regular 18-gon with an apothem of 13 mm

Answer 1

Solution:

A regular 18-gon is a polygon with 18 equal sides.

Thus, the area of a regular polygon is;

$\begin{gathered} A=na^2*\tan(\frac{180}{n}) \\ \\ \text{ Where;} \\ n=\text{ number of sides of the polygon} \\ \\ a=apothem \end{gathered}$

Thus;

$\begin{gathered} a=13mm,n=18 \\ \\ A=18(13^2)\tan(\frac{180}{18}) \\ \\ A=18(169)\tan(10) \\ \\ A\approx536.39mm^2 \end{gathered}$

The area of the regular 18-gon is 536.39 square millimeters