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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


Team Careers360 4th Jan, 2024
Answer (1)
Team Careers360 11th Jan, 2024

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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