Question

find the lateral area and surface area of a triangular prism with a height of 6 inches and a right triangular base with legs of 9 inches and 12 inches. round to the nearest tenth, if necessary.

Answer 1

• Lateral surface area is 216 in²
• Total surface area is 324 in²

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Find the hypotenuse c of the base using Pythagorean theorem:

• 
  `c=√(a^2+b^2)`

• 
  `c=√(9^2+12^2) =√(81+144)=√(225) =15`

Lateral surface area, three rectangular faces, is:

• LSA = Ph = (9 + 12 + 15)*6 = 36*6 = 216

Find base area, the area of two right triangles:

• A = 2*(1/2)(9)(12) = 108

Find total surface area:

• TSA = LSA + Base areas
• TSA = 216 + 108
• TSA = 324