The formula for the area of a regular polygon is as follows:
A=1/2*a*P
A=area
a=apothem
P=perimeter
Before we can begin solving the problem, we have to determine the side lengths and apothem.
Side lengths=24/6=4
How can we find the apothem? Draw a diagram.
Note: the central angle of a regular hexagon is 60 degrees.
Since the triangle in the diagram is a 30-60-90 kind of one, the length of the long leg (a) = sqrt 3*short leg.
a=2 sqrt 3
Now we can calculate the area:
A=1/2*2 sqrt 3*24
A=41.5692194 or about 41.57
