The base of a regular pyramid is a hexagon. What is the area of the base of the pyramid? Express your answer in radical form.

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1 Answer

Area of hexagon is #216sqrt(3)# #cm^2#

Explanation:

We know that the angle at #C# is 30 degrees, so half of the base must be #12/2# which is #6# as #sin(pi/6)=1/2#.
Finding #a# is a matter of Pythagorean,

as such #a^2+6^2=12^2#

or #a^2=144-36=108# and

#a=sqrt108=sqrt(6xx6xx3)=6sqrt(3)#.

Now, we have the height and half of the base, which means the area of #1/6#th of the hexagon will be #1/2bh# where #b=12# and #h=6sqrt3#.

The area of the hexagon therefore will be #6xx1/2bh#.

#=6xx1/2xx12xx6sqrt(3)=216sqrt(3)# #cm^2#