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.

oscar.a1551  May 14, 2018

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,


GYanggg  May 14, 2018

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

hectictar  May 15, 2018

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