MAT Exam 2022 Paper

Concept:For a square pyramid, total surface area $=$ base area $+$ lateral surface area.Lateral surface area $= \frac{1}{2} \times$ perimeter of base $\times$ slant height.Explanation:Side of the square base $= 32$ cm and height of pyramid $= 12$ cm.The slant height $l$ is obtained using the right triangle formed by the height, half the side, and the slant height.$l = \sqrt{(16)^2 + (12)^2} = \sqrt{256 + 144} = \sqrt{400} = 20$ cm.Perimeter of base $= 4 \times 32 = 128$ cm.Base area $= (32)^2 = 1024$ sq. cm.Lateral surface area $= \frac{1}{2} \times 128 \times 20 = 1280$ sq. cm.Total surface area $= 1024 + 1280 = 2304$ sq. cm.Answer:The total surface area is $2304$ sq. cm.Correct option: B. 2304 sq. cm.