SSC CGL 2025 Tier-I · 16 September 2025, Shift 1 · Quantitative Aptitude · Question 17 of 100

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 13 September 2026.

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If base perimeter = 40 cm, slant height = 10 cm, what is lateral surface area of square pyramid?

(a)260 cm²
(b)200 cm²
(c)400 cm²
(d)432 cm²

Answer

Why

Correct — B. The lateral faces of a square pyramid are four triangles, each with base = side and height = slant height.

Side of the square: 40 ÷ 4 = 10 cm
Area of one face: 1⁄2 × 10 × 10 = 50 cm²
Four faces: 4 × 50 = 200 cm² → option (b)

Shortcut: 1⁄2 × perimeter × slant height = 1⁄2 × 40 × 10 = 200 cm²

Why the others are wrong

(a)
260 cm² — 260 cm² is neither the lateral nor the total area: the four faces give 200 cm², and adding the 10 × 10 base gives 300 cm².
(c)
400 cm² — 400 cm² drops the 1⁄2 from the triangle area: perimeter × slant height = 40 × 10 = 400. Each face is a triangle, so halve it.
(d)
432 cm² — 432 cm² exceeds even the total surface area: four faces (200 cm²) plus the 10 × 10 base (100 cm²) make 300 cm².

Concept

Lateral surface area counts the slanted faces and leaves out the base. A square pyramid has four congruent triangular faces, each with the square's side as its base and the slant height as its height.

So LSA = 4 × 1⁄2 × side × slant height = 1⁄2 × perimeter × slant height. Total surface area adds the base: LSA + side².

Slant height, not vertical height. The slant height runs from the apex down the middle of a face to its base edge. The vertical height runs from the apex to the centre of the square and is shorter; it is the one used for volume (1⁄3 × base area × height).

Key facts

Lateral surface area of a regular pyramid = 1⁄2 × perimeter of base × slant height.
Total surface area = lateral surface area + base area.
A square with perimeter 40 cm has side 10 cm and area 100 cm².

Study next

Slant height from vertical height: l² = h² + (side⁄2)²Volume of a pyramid: 1⁄3 × base area × heightTotal surface area of a square pyramid

Common traps

Forgetting the 1⁄2 in the triangle area, which doubles the answer to 400 cm².
Adding the base when the question asks for the lateral surface alone.

17 Sep 2025, 12:30, Quant Q.15 runs the formula backwards: a square pyramid of base side 6 cm whose lateral area is twice its base area (2 × 36 = 72 cm²) has 1⁄2 × 24 × l = 72, so the slant height is 6 cm.

Related PYQs

No directly related past PYQ was found.

Topic: Right Prism, Right Circular Cone, Right Circular Cylinder, Sphere, Hemispheres, Rectangular Parallelepiped, Regular Right Pyramid with triangular or square base — all 99 SSC CGL questions on it, every solved shift.