Question

draw the net of a regular hexagonal pyramid with the side lengths of 5. if the volume of the pyramid is 200 what is the height of the pyramid?

Answer 1

any pyramid has a volume 1/3 of the base area times ht.

so here 1/3 * A * h = 200

or A * h = 600

now, for finding A, refer diagram

the hexagon is made up of 6 equilateral triangles of side length 5 each.
so A= 6 *area of each triangle.
now area of equilateral triangle is \[(\sqrt{3}/4)(side^{2})\]

so A = 6x 3 x (sq rt of 3) x5 x5 /2 = 225 * root3

h = 600/(225 * root 3)