GATE AG 2016 • Q64
MCQ • 2 Marks
Section 8: General Aptitude
Quantitative Aptitude
Subtopic: Numerical Computation
Question Statement:
A square pyramid has a base perimeter $x$, and the slant height is half of the perimeter. What is the lateral surface area of the pyramid?
Options:
-
(A) x²
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(B) 0.75 x²
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(C) 0.50 x²
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(D) 0.25 x²
Step-by-Step Solution & Explanation
• For a regular pyramid with base perimeter $P$ and slant height $l$, the total lateral surface area (LSA) consists of 4 triangular faces:
$\text{LSA} = \frac{1}{2} \times \text{Base Perimeter} \times \text{Slant Height}$
• Given:
- Base perimeter $P = x$
- Slant height $l = \frac{x}{2}$
• Substituting values:
$\text{LSA} = \frac{1}{2} \cdot x \cdot \left(\frac{x}{2}\right) = \frac{x^2}{4} = 0.25 x^2$
• Final Answer: (D) 0.25 x²
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