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      Question

      A square pyramid has a base side of 8 cm and a height of

      15 cm. Find the total surface area of the pyramid.
      A 256 cm² Correct Answer Incorrect Answer
      B 312.3 cm² Correct Answer Incorrect Answer
      C 320 cm² Correct Answer Incorrect Answer
      D 368 cm² Correct Answer Incorrect Answer

      Solution

      Base area = side² = 8² = 64 cm². Slant height (l) = √[(side/2)² + height²]  = √[(8/2)² + 15²] = √[4² + 15²]  = √[16 + 225] = √241 ≈ 15.52 cm. Lateral surface area = (1/2) * perimeter * slant height = (1/2) * (4 * side) * l  = (1/2) * (4 * 8) * 15.52 = 248.32 cm². Total surface area = Base area + Lateral surface area = 64 + 248.3 = 312.3 cm². Correct option: b) 312.3 cm²

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