What is the area of a regular hexagon with an apothem of 6m in length?

Solution:

Given, an apothem of a regular hexagon is 6m.

We have to find the area of a regular hexagon.

From the image,

The regular hexagon is formed by six triangles whose sides are two circles' radii and the hexagon’s side.

The angle of each of these triangles is equal to (360/6) = 60°.

So, these triangles are equilateral.

The apothem divides equally each one of the equilateral triangles into right triangles whose sides are the circles' radii, apothem, and half of the hexagon’s side.

So, tan 60° = (opposite / adjacent) = Apothem/(side/2)

√3 = 2(Apothem)side

√3 = 2(6)/side

Side = 12/√3

Side = 4√3

Area of hexagon = 6(area of equilateral triangle).

Area = 6(bh/2)

Area = 6(4√3)(6)/2

= 36(4√3)/2

= 144√3/2

= 72√3 square meters.

Therefore, the area is 72√3 square meters.

What is the area of a regular hexagon with an apothem of 6m in length?

summary:

The area of a regular hexagon with an apothem of 6m length is 72√3 square meters.