Question

Find the area of a regular hexagon with the given measurement

48-inch perimeter
A = sq. in.

Answer 1

`Area = (3 √(3) )/(2) s^(2) \\ \\ (48)/(6) = 8=s \\ \\ Area =(3 √(3) )/(2) 64 \\ \\ Area =166.28`

Answer 2

Area of a regular hexagon is given by:

`A = (3√(3))/(2)a^2` .....[1]

where,

A is the area of a regular hexagon

a is the side of the hexagon.

As per the statement:

Perimeter of a regular hexagon is 48 inch.

Perimeter(P) of a regular hexagon is given by:

`P=6a`

Substitute the given values we have;

`48 = 6a`

Divide both sides by 6 we have;

`8 = a`

or

a = 8 inch.

Substitute the value of a = 8 inches in [1] we have;

`A = (3√(3))/(2)(8)^2`

⇒
`A = 3√(3) \cdot 32 = 96√(3)`

Therefore, the area of a regular hexagon is
`A = 96√(3)` sq. in