Question

What’s the area of the regular polygon picture below

Answer 1

Given:

Regular polygon.

Side length = 18 in

To find:

The area of the regular polygon.

Solution:

Let us first find the apothem (length from center to side).

Apothem formula:

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

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

number of sides (n) = 6

$a=\frac{18}{2 \tan \left(\frac{180^\circ}{6}\right)}$

$a=\frac{9}{\tan (30^\circ)}$

The value of $\tan \left(30^{\circ}\right)=\frac{\sqrt{3}}{3}$

$a=\frac{9}{\frac{\sqrt{3}}{3}}$

$a=9 \sqrt{3}$ in

Area of regular polygon:

$A=\frac{1}{2} \times p \times a$

where p is perimeter of polygon and a is apothem.

$A=\frac{1}{2} \times (6\times 18) \times 9\sqrt{3}$

$A=54 \times 9\sqrt{3}$

$A=841.78$ square inches.

The area of the regular polygon is 841.78 square inches.