Question

A prism has isosceles triangle bases with leg lengths of 5 inches, 5 inches, and 8 inches, and a height of 3 inches. The distance between the bases is 12 inches. Find the surface area. Show your work, please. Thank you in advance for assisting me with this Math problem

Answer 1

The total surface area is the sum of the lateral area and the area of the bases.

The area of each triangular base is
  A = (1/2)bh
  A = (1/2)(8 in)(3 in) = 12 in²

The lateral area is the product of the perimeter of the base and the distance between bases.
  A = Ph
  A = (5 in +5 in +8 in)(12 in) = 216 in²

Then the total area is
  2*base area + lateral area
  = 2(12 in²) +(216 in²)
  = 240 in²

The surface area of the prism is 240 in².