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.
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,
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