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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.

 Apr 10, 2019
 #1
avatar+109560 
+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

 

 

cool coolcool

 Apr 10, 2019
 #2
avatar+54 
+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

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