A square pyramid has a base perimeter b, and the slant height is half of the perimeter. What is the lateral surface area of the pyramid? A. b^2/2 B. 0.75*b^2 C. 0.50*b^2 D. 0.25*b^2

GATE 2016 · General Aptitude · Geometry · medium

Answer: Lateral surface area = b^2/4 = 0.25*b^2

1. Identify each side of the square base: side = b/4
2. Identify slant height: l = b/2
3. Compute area of one triangular face: Area of one face = (1/2) * (b/4) * (b/2) = b^2/16
4. Compute total lateral surface area: Lateral SA = 4 * (b^2/16) = 4*b^2/16 = b^2/4 = 0.25*b^2