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=(s)/(2 \tan \left((180^\circ)/(n)\right))`

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

number of sides (n) = 6

`$a=(18)/(2 \tan \left((180^\circ)/(6)\right))`

`$a=(9)/(\tan (30^\circ))`

The value of
`\tan \left(30^(\circ)\right)=(√(3))/(3)`

`$a=(9)/((√(3))/(3))`

`a=9 √(3)` in

Area of regular polygon:

`$A=(1)/(2) * p * a`

where p is perimeter of polygon and a is apothem.

`$A=(1)/(2) * (6* 18) * 9√(3)`

`$A=54 * 9√(3)`

`$A=841.78` square inches.

The area of the regular polygon is 841.78 square inches.