What radius of a circle is required to inscribe a regular hexagon with an area of 166.28 in2 and an apothem of 6.928 in?

If you want to inscribe a polygon inside a circle, you have a formula that doesn't have to use the apothem. The formula is:

A = (nr²/2) sin (360/n)

Since the polygon is a hexagon, it has 6 sides. Thus, n = 6. Knowing the area, we can determine the radius of the circle, r.

166.28 = (6r²/2) sin (360/6)

r = 8 inches

Thus, the radius of the circle is 8 inches.