Question

find the volume of a pyramid with an equilateral triangle as a base that has a side length of 12 in. The height of the pyramid is 10 in

Answer 1

Surface pyramid with an equilateral triangle as a base = 3 * surface triangle + surface equilateral triangle
Surface triangle = 0.5bh
b=12 in
h=0.5*sqrt(3)*12 = 6sqrt(3) in
Surface triangle = 0.5 * 12 * 6*sqrt(3)=36sqrt(3) in²
Surface equilateral triangle = 0.5 * sqrt(3) * 12=6sqrt(3) in²
Surface pyramid = 3 * 36sqrt(3) + 6sqrt(3) = 108sqrt(3) +6 sqrt(3)=114 sqrt(3) in²