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The base of a regular pyramid is a hexagon.

What is the area of the base of the pyramid?

Enter your answer in the box. Express your answer in radical form.

 May 14, 2018
 #1
avatar+972 
+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
avatar+7350 
+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          smiley

 May 15, 2018

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