Question

A triangular pyramid has faces that are all equalatetal triangles. Each side length is 16 cm. What is the surface area of the pyramid?

Answer 1

So you have a tetrahedron

area of one of the triangles
= (1/2)(16)(16)sin60
= 128(√3/2) = 64√3

Counting the base there are 4 faces, so

surface area = 4(64√3) = 256√3 = appr 443.4 cm^2

If you don't want to count the base, multiply by 3 instead of by 4

Answer 2

four sides, area=4(1/2 b h)

but you can find h from
tan60=h/(b/2) or h=base*tan60 /2

area=2(bh)=2(b*b*tan60/2)=b^2 tan60

check my math.