Answer:
36√3 + 144
Explanation:
Given that,
base of the pyramid is an equilateral triangle with sides = 12
Formula to calculate total surface area of pyramid
[Base Area] + 1/2 × Perimeter × [Slant Length]
Base Area
1/2 (height) (base)
1/2 (√12²-6²)(12)
6(6√3)
36√3
perimeter of base
sum of all sides = 12 + 12+ 12
= 36
slant height = √10²-6²
= 8
put all these values in the formula above
36√3 + 1/2(36)(8)
36√3 + 144
Total area for the pyramid with the equilateral base =
36√3 + 144