SSC CGL 2025 Tier-I · 17 September 2025, Shift 2 · Quantitative Aptitude · Question 15 of 99

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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A square pyramid has lateral surface area equal to twice the base area. If base side = 6 cm, find slant height.

(a)6 cm
(b)5 cm
(c)4 cm
(d)2 cm

Answer

Why

Correct — A. The lateral surface is four triangular faces, each with base = the side a and height = the slant height l.

Square the side: base area = 6² = 36 cm²
Double it, as the stem says: lateral area = 72 cm²
Share over 4 faces: 72 ÷ 4 = 18 cm² each

Triangle area: ½ × 6 × l = 3l
Solve: 3l = 18, so l = 6 cm → option (a)

Why the others are wrong

(b)
5 cm — Slant height 5 cm gives a lateral area of 12 × 5 = 60 cm², which is 5⁄3 of the 36 cm² base, not double it.
(c)
4 cm — Slant height 4 cm gives 12 × 4 = 48 cm² of lateral surface, 4⁄3 of the base. Doubling the 36 cm² base needs 72 cm², so l = 6 cm.
(d)
2 cm — Slant height 2 cm gives just 24 cm² of lateral surface, less than the base itself. The condition asks for 72 cm².

Concept

Lateral surface of a regular pyramid = ½ × base perimeter × slant height. For a square base of side a, that is ½ × 4a × l = 2al. With a = 6 cm, it is 12l.

Setting 2al equal to 2 × a² cancels 2a from both sides and leaves l = a. So whenever the lateral surface is double the base, the slant height equals the base side.

Slant height runs along a face, from the apex to the midpoint of a base edge. The vertical height is shorter: √(6² − 3²) = √27 ≈ 5.2 cm. The stem asks the slant height.

Key facts

Lateral surface area of a regular pyramid = ½ × perimeter of base × slant height.
Square pyramid of side a: lateral area 2al, base area a².
Slant height l, vertical height h and half the side a⁄2 form a right triangle: l² = h² + (a⁄2)².

Study next

Total surface area of a square pyramid, a² + 2alSlant height from vertical height through l² = h² + (a⁄2)²Volume of a pyramid, ⅓ × base area × vertical height

Common traps

Dropping the ½: perimeter × slant = 24l = 72 gives l = 3 cm.
Confusing the slant height with the vertical height, about 5.2 cm here.

The same lateral-area formula decides 16 Sep 2025, 09:00, Quant Q.17: a base perimeter of 40 cm and slant height of 10 cm give ½ × 40 × 10 = 200 cm².

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.