We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
29
2
avatar+626 

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+99580 
+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+46 
+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

6 Online Users