GATE 2026 AR — Architecture – Question 49
A 4×4 cm square prism, 20 cm high, stands on HP with its faces 45° to VP. The cutting plane perpendicular to VP is shown in the plan and elevation. Find total area of the four vertical faces below the cut, in cm² as an integer.
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Correct answer: 144 to 144
Explanation
Read the cut heights at the four vertical edges from elevation:6, 9, 12, 9 cm. Each vertical face is a trapezoid of width 4 cm. Summing their areas gives 4×½[(6+9)+(9+12)+(12+9)+(9+6)]=144 cm². Only the lateral vertical faces are requested, excluding the base and inclined cut surface.