Find the total area for the pyramid with the equilateral base.

t. a. =

T.A. = 144 + 36√3 units²

Step-by-step 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

25/6

step-by-step explanation:

you multiply 4 by the denominator (4*6=24) and add it to the numerator which makes it 25/6.