SSC CGL 2025 Tier-II · Paper-I, 19 January 2026 · Mathematical Abilities · Question 25 of 150

We transcribed this text from the pictures of a candidate's response sheet for this paper; the answer is the key SSC marked with a green tick on that sheet. Solution last reviewed 11 September 2026.

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The base of a right prism is an isosceles trapezium with parallel sides measuring 10 cm and 20 cm, and non-parallel sides measuring 13 cm each. The volume of the prism is 3240 cm³. What is the total surface area of the prism?

(a)1940 cm²
(b)1368 cm²
(c)1620 cm²
(d)2120 cm²

Answer

Why

Correct — B. Find the trapezium's height, then the prism's length, then add up the faces.

Overhang on each side: (20 − 10) ÷ 2 = 5 cm
Trapezium height: √(13² − 5²) = √144 = 12 cm
Base area: ½ × (10 + 20) × 12 = 180 cm²

Prism length: 3240 ÷ 180 = 18 cm
Base perimeter: 10 + 20 + 13 + 13 = 56 cm
Lateral area: 56 × 18 = 1008 cm²

Total: 1008 + 2 × 180 = 1368 cm² → option (b)

Why the others are wrong

(a)
1940 cm² — 1940 cm² would leave 1940 − 1008 = 932 cm² for the two ends, 466 cm² each. Each trapezium end is 180 cm².
(c)
1620 cm² — 1620 cm² would need each end to be (1620 − 1008) ÷ 2 = 306 cm². A trapezium of height 12 gives ½ × 30 × 12 = 180 cm².
(d)
2120 cm² — 2120 cm² overshoots: with the side faces fixed at 56 × 18 = 1008 cm², the two ends would have to total 1112 cm², but they total 360 cm².

Concept

A right prism's total surface area = lateral area + 2 × base area, and its side faces unroll into one rectangle of base perimeter × length.

The volume supplies the missing length: length = volume ÷ base area.

For the isosceles trapezium, drop perpendiculars from the ends of the 10 cm side. They cut off two right triangles with base (20 − 10)⁄2 = 5 cm and hypotenuse 13 cm, so the height is 12 cm: the 5-12-13 triple.

The volume, 3240 cm³, is there to recover the prism's length. It does not enter the surface-area sum itself.

Key facts

Lateral surface area of a right prism = base perimeter × height (length).
Total surface area of a right prism = lateral area + 2 × base area.
Area of a trapezium = ½ × (sum of parallel sides) × height.
5-12-13 is a Pythagorean triple: 5² + 12² = 13².

Study next

Surface area of a prism on a right-triangle or rhombus baseHeight of an isosceles trapezium from its four sidesHow volume and surface area change when a prism's length changes

Common traps

Taking the slanting 13 cm side as the trapezium's height, which makes the base area 195 cm².
Adding one base instead of two to the lateral area: 1008 + 180 = 1188 cm².

Here the volume is given so that the length must be worked out first. Lateral area as base perimeter × height is asked directly at 15 Sep 2025, 12:30, Quant Q.19 (lateral area 240 cm², height 8 cm, base perimeter 30 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 56 SSC CGL questions on it, every solved shift.