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# 4.10

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The base of a regular pyramid is a hexagon.

What is the area of the base of the pyramid?

May 14, 2018

#1
+985
+3

Once again, we use the 30 - 60 -90 rule.

The hypotenuse is twice the length of the side opposite of the 30 degree angle.

Therefore the side opposite of the 30 degree angle is 12/2 = 6

We can use the Pythagorean theorem, to find the length of a.

12^2 - 6^2 = a^2

a^2 = 108

a = √108 = 6√3

I hope this helped,

Gavin

May 14, 2018
#2
+8118
+1

And to find the area of the base...

The base is a regular hexagon, and  12  of the little outlined triangle would fill it exactly. So

area of base  =  12(area of little triangle)

area of little triangle  =  (1/2)(base)(height)

If we let the base be the side opposite the 30° angle and the height be  a , then the base is  6 cm  and the height is  6√3 cm , as Gavin found.

area of little triangle  =  (1/2)(6)(6√3)  sq cm

area of little triangle  =  18√3  sq cm

area of base  =  12(18√3)  sq cm

area of base  =  216√3  sq cm

May 15, 2018