What is the sq footage of 12' hexagon?

Answer 1

What is the 12 foot?

It could be the radius or diameter of the inscribed or circumscribed circles.

Or it could be the length of each side.

There are thus three solutions depending on above parameters.

The hexagon must be a regular hexagon.

Let R = radius of circumscribed circle in feet

Let r = radius of inscribed circle in feet

Let s = length of one of the sides in feet

Then area in square feet = 2.598*s2 or 2.598*R2 or 3.464*r2

(R = s = 1.155*r where 1.155 = 1 / sin 60 degr.)

The shortened formula 2.598*s2 is obtained as follows:

There are six equilateral triangles in a regular hexagon when three lines are drawn connecting opposite corners.

Therefore the area is the sum of the six triangles.

Each triangle area is 1/2 base x height.

Therefore each A = 0.5s x (sqrt of 3 x 0.5s) = 0.25s2 x sqrt of 3 = 0.433s2

So 6 triangles will be 6 x 0.433s2 = 2.598s2