What is the area, in square units, of a regular hexagon inscribed in a circle whose area is \(324\pi\) square units? Express your answer in simplest radical form.

Logic Apr 10, 2019

#1**+2 **

Not too difficult.....the radius of the circle, r = the side of the hexagon, s...so

324 pi = pi* r^2

324 = r^2

18 = r

The hexagon = six equilateral triangles ....its area =

6 * √3 /4 * s^2 =

(3/2)√3 * 324 =

486√3 units^2

CPhill Apr 10, 2019

#2**+1 **

That looks great to me! In general, the formula for a hexagon is \(\frac{3\sqrt{3}}{2}s^2\) .

neworleans06
Apr 10, 2019