Find the volume of a hexagonal pyramid with the base edge of 8 and 12 being the height?

Question

Find the volume of a hexagonal pyramid with the base edge of 8 and 12 being the height?

Answer 1

volume of pyramid=1/3 * base area * height

base area = 8*8 + 2(1/2 * 8 * 8sin60)

draw the hexagon....each angle is equal to 60

angle=360/6=60

the rest is simple trigonometry..

Answer 2

The volume of a pyramid is Bh/3, where B is the area of the base and h is the height. The area of the base can be found by ap/2, where a is the apothem of the hexagon and p is the perimeter. Since hexagons have six sides, the perimeter of this hexagon is 8*6 = 48 units. Now, the apothem of any regular hexagon can be found by s/2*sqrt3, where s is the side of the hexagon, so the apothem of this hexagon is 4sqrt3. And now you can find the volume:

V = Bh/3

V = ap/2 (h) / 3

V = 4sqrt3(48) (12) / 3

V = 192sqrt3 (12) / 3

V = 2,034sqrt3 / 3

V = 768sqrt3 or about 1,330.215 cubic units <===ANSWER