Answer:
T.A. = 144 + 36√3 units²
Explanation:
∵ The total surface area of the pyramid = the sum of the area of
the four faces (one base and 3 side faces)
∵ The 3 side faces have the same dimensions 12 , 10 , 10
∴ the area of the 3 faces = 3 × 1/2 × 12 × h
∵ The height of each triangle is ⊥ to its base
∵ The triangle are isosceles
∴ The height bisects the base
∴ h² = 10² - 6² = 64
∴ h = √64 = 8
∴ The area of the 3 triangles = 3 × 1/2 × 12 × 8 = 144 units²
∵ The base is equilateral Δ with side length 12
∵ Area equilateral triangle = 1/4 × s² × √3
∴ The area of the base = 1/4 × (12)² × √3 = 36√3 units²
∴ T.A. = 144 + 36√3 units²