What would be the formula for the area of a regular hexagon?

Question

 I was confused if I use the formula of a trapezoid and incorporate the numbers, but it is inscribed in a circle and only gave us the radius of the circle, which is 18in.

Answer 1

The regular hexagon can be subdivided into 6 congruent equilateral triangles, each side measuring 18 in (the radius).

 

Now turn your attention to ONE of those equilateral triangles; construct the altitude, which will bisect a central angle. This creates a 30-60-90 triangle, having hypotenuse r = 18 inches and its other leg 9 inches (opp. 30^o). This enables you to calculate the length of the altitude (it's 9√3).

 

What is the area of ONE of those equilateral triangles?  Answer ½•base•altitude = ½•18•9√3.

Simplify this number, and then multiply by 6 to get entire area of the regular hexagon of r = 18.