SSC CGL 2025 Tier-I · 21 September 2025, Shift 1 · Quantitative Aptitude · Question 10 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.

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 hexagon is drawn inside a circle with a radius of 21 cm. Determine the approximate area of the hexagon.

(a)1145 cm²
(b)1845 cm²
(c)165 cm²
(d)172 cm²

Answer

Why

Correct — A. Read the hexagon as regular with its corners on the circle. It then splits into six equilateral triangles whose sides equal the radius.

Side of each triangle = radius = 21 cm
One triangle: (√3⁄4) × 21² = (√3⁄4) × 441 ≈ 190.96 cm²
Six triangles: 6 × 190.96 ≈ 1145.8 cm²

Same in one line: (3√3⁄2) × 441 ≈ 2.598 × 441 ≈ 1145.8
Nearest choice: 1145 cm² → option (a)

Why the others are wrong

(b)
1845 cm² — 1845 cm² is bigger than the whole circle: πr² = (22⁄7) × 441 = 1386 cm². A hexagon drawn inside the circle cannot cover more than the circle itself.
(c)
165 cm² — 165 cm² is less than a single one of the six triangles, (√3⁄4) × 21² ≈ 191 cm². The hexagon is made of six such triangles.
(d)
172 cm² — 172 cm² is also smaller than one equilateral triangle of side 21 (≈191 cm²), so it cannot be six of them. The true area is about 6 × 191 ≈ 1146 cm².

Concept

A regular hexagon inscribed in a circle has side equal to the radius. Joining the centre to the six corners makes six triangles with two radii as sides and a 60° angle at the centre (360° ÷ 6), so each is equilateral.

Area = 6 × (√3⁄4)r² = (3√3⁄2)r² ≈ 2.598r².

A sanity check: the hexagon is about 83% of its circle (2.598 ÷ 3.1416 ≈ 0.827), and 0.827 × 1386 ≈ 1146.

The stem says only "a hexagon" drawn inside the circle. The keyed 1145 cm² is the area of a regular hexagon with its corners on the circle, so read it that way; an irregular hexagon would not give one fixed area.

Key facts

A regular hexagon inscribed in a circle of radius r has side r
Area of an equilateral triangle of side a = (√3⁄4)a²
Area of a regular hexagon of side a = (3√3⁄2)a² ≈ 2.598a²

Study next

Area between a circle and its inscribed regular hexagon: πr² − (3√3⁄2)r²Regular hexagon from its perimeter (side = perimeter ÷ 6)Circle inscribed in a regular hexagon: its radius is (√3⁄2) × side

Common traps

Using the circle's area πr² (≈1386 cm² here) in place of the hexagon's
Stopping at one equilateral triangle (≈191 cm²) and not multiplying by six

Also asked 21 Sep 2025, 16:00, Quant Q.9: a regular hexagon inscribed in a circle of radius 14 cm, where (3√3⁄2) × 196 ≈ 509.2 gives the keyed 509.21 cm².

That stem says regular and inscribed outright; this one leaves both to be assumed.

Related PYQs

No directly related past PYQ was found.

Topic: Circle and its chords, tangents, angles subtended by chords of a circle, common tangents to two or more circles — all 140 SSC CGL questions on it, every solved shift.