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

#1**+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

GYanggg
May 14, 2018

#2**+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

hectictar
May 15, 2018