Question

A regular hexagon is shown below.

If the length of each side of the hexagon is 30 cm, and the radius of the hexagon is also 30 cm, what is the hexagon's approximate area? Round your answer to the nearest tenth.

PLEASE DRAW IT OUT

Answer 1

area = 2,338.2cm^2

Explanation:

There is a simple formula for finding the area of a regular hexagon via its side length, but I'm assuming your teacher would like it geometrically considering you asked me to draw it out!

See attached image.

Find the height of the shaded triangle using the Pythagorean theorem:

15^2 + h^2 = 30^3

225 + h^2 = 900

h^2 = 675

h = ~25.98 cm

Find the area of the shaded triangle using 1/2bh:

1/2(15)(25.98) = 194.85

There are 12 such triangles in the hexagon.

12(194.85) = 2,338.2