Question

Find the area of the regular polygon. Round to the nearest tenth.

Answer 1

Given:

Side length = 12 in

To find:

The area of the regular polygon.

Solution:

Number of sides (n) = 6

Let us find the apothem using formula:

$a=\frac{s}{2 \tan \left(\frac{180^\circ}{n}\right)}$

where s is side length and n is number of sides.

$a=\frac{12}{2 \tan \left(\frac{180^\circ}{6}\right)}$

$a=\frac{6}{ \tan (30^\circ)}$

$a=\frac{6}{ \frac{1}{\sqrt{3} }}$

$a=6\sqrt{3}$

Area of the regular polygon:

$A=\frac{1}{2}(\text { Perimeter })(\text { apothem })$

$A=\frac{1}{2}(6 \times 12)(6\sqrt{3} )$

$A=\frac{1}{2}(72)(6\sqrt{3} )$

$A=216 \sqrt{3}$

$A=374.1$ in²

The area of the regular polygon is 374.1 in².