Question : What is the total surface area of a pyramid whose base is a square with a side 8 cm and the height of the pyramid is 3 cm?
Option 1: 169 cm2
Option 2: 121 cm2
Option 3: 144 cm2
Option 4: 184 cm2
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Correct Answer: 144 cm 2
Solution : Given, The side of the square base = 8 cm and the height of the pyramid = 3 cm The slant height (l) of the pyramid needs to be evaluated, ⇒ l 2 = ($\frac{\text{side}}{2}$) 2 + (Height) 2 ⇒ l 2 = 4 2 + 3 2 ⇒ l 2 = 16 + 9 ⇒ l 2 = 25 ⇒ l = 5 cm The total surface area of the pyramid = (Base Area) + $\frac12$ × (Perimeter of base) × (Slant height) = 64 + $\frac12$ × 32 × 5 = 64 + 16 × 5 = 64 + 80 = 144 cm 2 Hence, the correct answer is 144 cm 2 .
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