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SSC CGL 2024 PYQ — Question 56

SSC CGL - 10 Sep 2024 - Shift 1 • Quantitative Aptitude • Q56

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The side of an equilateral triangle is 28 cm. Taking each vertex as the centre, a circle is described with a radius equal to half the length of the side of the triangle. Find the area of that part of the triangle which is not included in the circles (use π = 22722\over7 and 3\sqrt 3 = 1.73).

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 31.08 cm2.

Radius of the circle, r = 28228 \over 2 =14 cm

Each angle of an equilateral triangle = 60°

Part of the triangle covered by 3 circles at the corners = 3 × 60° = 180°

Now, the Area which is not included in the circle = Area of the triangle - Area of the semi-circle

34×(a)2−π×r22{\sqrt{3} \over 4} \times (a)^2 - {\pi \times r^2 \over 2}

⇒ 34×28×28−227×14×142{\sqrt{3} \over 4} \times 28 \times 28 - {{22 \over 7} \times 14 \times 14 \over 2}

⇒ 1.73×7×28−22×141.73 \times 7 \times 28 - {22 \times 14}

⇒ 339.08 - 308 = 31.08 cm2