SSC CGL 2025 Tier-I · 21 September 2025, Shift 3 · Quantitative Aptitude · Question 9 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 11 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 regular hexagon is inscribed inside a circle of radius 14 cm. Find the area of the hexagon.

(a)438.54 cm²
(b)509.21 cm²
(c)598.45 cm²
(d)638.76 cm²

Answer

Why

Correct — B.
A regular hexagon in a circle splits into six equilateral triangles whose sides equal the radius.

Side of each triangle: 14 cm
One triangle: (√3⁄4) × 14² = (√3⁄4) × 196 = 49√3
Six triangles: 6 × 49√3 = 294√3

With √3 ≈ 1.732: 294 × 1.732 = 509.208 ≈ 509.21 cm² → option (b)

Why the others are wrong

(a)
438.54 cm² — 438.54 cm² is only about 71% of the circle's 616 cm². An inscribed regular hexagon covers about 83% of its circle, which puts it near 509 cm².
(c)
598.45 cm² — 598.45 cm² is about 97% of the circle's 616 cm², leaving almost nothing for the six circular segments outside the hexagon. The hexagon covers about 83%.
(d)
638.76 cm² — 638.76 cm² is more than the whole circle, (22⁄7) × 14² = 616 cm². A figure drawn inside a circle cannot have more area than the circle.

Concept

In a regular hexagon inscribed in a circle, each side subtends 360° ÷ 6 = 60° at the centre. Joining the centre to the six vertices gives six triangles, each with two sides equal to the radius and 60° between them, so each is equilateral.

Area of a regular hexagon of side a = 6 × (√3⁄4)a² = (3√3⁄2)a².

The option's 509.21 comes from √3 ≈ 1.732. With √3 ≈ 1.7320508, 294√3 ≈ 509.22; the two differ only in the second decimal, and every other option is at least 70 cm² away.

Key facts

A regular hexagon inscribed in a circle has side equal to the radius
Area of a regular hexagon of side a = (3√3⁄2)a²
Area of an equilateral triangle of side a = (√3⁄4)a²
An inscribed regular hexagon covers 3√3⁄(2π) ≈ 83% of its circle

Study next

Area of a circular segment cut off by a chord equal to the radiusArea of a square or equilateral triangle inscribed in a circleInterior angle of a regular n-sided polygon, (n − 2) × 180° ⁄ n

Common traps

Taking the side as the diameter, 28 cm, instead of the radius, 14 cm
Stopping at one triangle's area, 49√3 ≈ 84.87 cm², and forgetting the × 6

14 Sep 2025, 12:30, Quant Q.23 rests on the same fact: a chord that forms an equilateral triangle with two radii cuts off a 60° segment of a clock of radius 20 cm, keyed 2.88% of its area.

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 84 SSC CGL questions on it, every solved shift.