Question

Find the area of the regular polygon.Round to the nearest tenth.16 ft​

Answer 1

Given:

Given that the side of the regular polygon is 16 feet.

We need to determine the area of the polygon.

Area of the polygon:

The area of the polygon can be determined using the formula,

$Area =\frac{s^2 n}{4 \ tan \frac{180}{n}}$

where n is the number of sides,

s is the side length.

Substituting n = 3 and s = 16, we get;

$Area =\frac{16^2 (3)}{4 \ tan \frac{180}{3}}$

Simplifying, we get;

$Area =\frac{(256) (3)}{4 \ tan \ 60}$

$Area = \frac{768}{6.928}$

Dividing, we get;

$Area = 110.85$

Rounding off to the nearest tenth, we have;

$Area = 110.9$

Thus, the area of the regular polygon is 110.9 square units.