Question

If the perimeter of the regular hexagon given below is 90 sq. in, calculate its area.

• A. 159.75 sq. in
• B. 266.25 sq. in
• C. 213 sq. in
• D. 319.5 sq. in

Answer 1

The correct option is D 319.5 sq. in

Given,
Perimeter of the regular hexagon = 90 in
$\because$ Perimeter of a regular hexagon = 6 x side of hexagon
$\Rightarrow$ 6 x side of the hexagon = 90

$\text{Side of the hexagon=}\frac{90}{6}=15\text{in}$


Since, a regular hexagon can be divided into 6 congruent triangles, area of regular hexagon is 6 times the area of each triangle.

Area of regular hexagon = 6 x Area of triangle AOF

$\text{Area of triangle AOF =}\frac{1}{2}\times base\times height$
$=\frac{1}{2}\times 15\times 7.1$
$=53.25\text{sq. in}$

⇒ Area of regular hexagon = 6 x 53.25
= 319.5 sq. in