Find the area of a regular hexagon with the given measurement 48-inch perimeter A = sq. in.

Solution:

An equilateral triangle is a regular polygon with 3 equal sides with each angle equal to 60°.

The area of a regular hexagon is

A = (3√3)/2 × s², where s is the side length

The 6-sided figure will have a side length that is 1/6 of the perimeter.

S = 48/6 = 8 in

A = (3√3)/2 × (8)² = 96√3 in²

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

Find the area of a regular hexagon with the given measurement 48-inch perimeter A = sq. in.

Symmetry:

The area of a regular hexagon with the given measurement 48-inch perimeter is A = 96√3 sq. in.