SSC CGL 2025 Tier-I · 23 September 2025, Shift 3 · Quantitative Aptitude · Question 14 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.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. From 2025 the candidate response sheet prints every question and option as a picture, so the text here is transcribed from those pictures for this shift and checked against them independently; where the layout carries meaning, the picture is shown as well. Each answer is the key SSC colour-marked on that sheet. SSC released a tentative key for challenge and later its final one, both only to candidates behind a login, and the sheet does not say which of the two it carries. The solutions are written by UnlockIAS.

A prism with a parallelogram base has base area 80 cm² and height 12 cm. If its lateral surface area is 384 cm², what is the perimeter of the base?

(a)24 cm
(b)32 cm
(c)36 cm
(d)40 cm

Answer

Why

Correct — B. The side faces of a prism unroll into one rectangle: its length is the perimeter of the base, its width the height.

Lateral surface area = perimeter × height
384 = perimeter × 12
Perimeter = 384 ÷ 12 = 32 cm → option (b)

The base area of 80 cm² is not used.

Why the others are wrong

(a)
24 cm — 24 cm × 12 cm = 288 cm² of side faces, short of the 384 cm² given.
(c)
36 cm — 36 cm × 12 cm = 432 cm² of side faces, more than the 384 cm² given.
(d)
40 cm — 40 cm × 12 cm = 480 cm² of side faces, well past the 384 cm² given.

Concept

A right prism's side faces are rectangles of the same height. Laid side by side they make one long rectangle: height × (sum of the base's sides), which is height × perimeter.

That holds for any base, triangle, parallelogram or hexagon. The base area enters the volume (base area × height) and the total surface area (lateral area + 2 × base area), not the lateral area.

The printed numbers do not fit together. A parallelogram with a 32 cm perimeter has two adjacent sides adding to 16 cm, so its area is at most 8 × 8 = 64 cm², the square. No such base can have an area of 80 cm².

The lateral area and height alone fix the perimeter at 32 cm, so the key stands. The stem also omits the word 'right'. The formula reads the height as the height of the side faces.

Key facts

Lateral surface area of a right prism = perimeter of base × height.
Total surface area of a prism = lateral surface area + 2 × base area.
Volume of a prism = base area × height.
For a fixed perimeter, the square has the largest area of any parallelogram.

Study next

Total surface area of prisms with triangular and trapezium basesVolume of a prism when its base area or height changes by a percentageLateral surface area of a regular pyramid: ½ × perimeter × slant height

Common traps

Treating 384 cm² as the total surface area and taking off 2 × 80 cm² for the two bases: lateral means the side faces alone.
Hunting for the parallelogram's side lengths from its area: the lateral area gives the perimeter directly.

The same inversion, lateral area and height to perimeter, is 15 Sep 2025, 12:30, Quant Q.19: 240 ÷ 8 = 30 cm.

The forward direction is 24 Sep 2025, 12:30, Quant Q.14: a 5 : 12 : 13 base with perimeter 60 cm and height 8 cm gives 60 × 8 = 480 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.