Answer
Area of a regular hexagon is given by:
[tex]A = \frac{3\sqrt{3}}{2}a^2[/tex] .....[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:
[tex]P=6a[/tex]
Substitute the given values we have;
[tex]48 = 6a[/tex]
Divide both sides by 6 we have;
[tex]8 = a[/tex]
or
a = 8 inch.
Substitute the value of a = 8 inches in [1] we have;
[tex]A = \frac{3\sqrt{3}}{2}(8)^2[/tex]
⇒[tex]A = 3\sqrt{3} \cdot 32 = 96\sqrt{3}[/tex]
Therefore, the area of a regular hexagon is[tex]A = 96\sqrt{3}[/tex] sq. in