The area of a regular hexagon is 55 in^2. Find the length of a side. Round your answer to the nearest tenth. I know the answer is 4.6 in., but I have no idea how to solve it.

polygon area = n*side length^2 / [4*tan(180/n)]
side length^2 = polygon area * [4*tan(180/n)] / n
where n is the number of sides
side length^2 = 55 sq inches * (4*tan(180/6)) / 6
side length^2 = 55 sq inches * 4 * tan (30) / 6
side length^2 = (55 sq inches * 4 * 0.57735) / 6
side length^2 = 127.017 / 6
side length^2 = 21.1695
side length = square root ( 21.1695 )
side length = 4.6010324928

MrRoyal MrRoyal · Answer 2 · 2022-04-22T12:36:04+02:00

The side length of the regular hexagon is 4.6 inches

How to determine the side length?

The area is given as:

Area = 55 in^2

The area of a regular hexagon is calculated using:

A = 1.5√3 a²

Where a is the side length.

So, we have:

55 = 1.5√3 a²

Divide both sides by 1.5√3

a² = 21.17

Take the square root of both sides

a = 4.6

Hence, the side length of the regular hexagon is 4.6 inches