2018 · Q17
Consider the following diagram: [An equilateral triangle inscribed in a circle of radius 1 unit; the circular segment below the base of the triangle is shaded.] An equilateral triangle is inscribed in a circle of radius 1 unit. The area of the shaded region, in square unit, is
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- Aπ/3 − √3/4
- Bπ/3 − 1/2
- Cπ/3 − 3/4
- Dπ/3 − 1
Explanation
The base of the inscribed equilateral triangle subtends 120° at the centre, so the circular sector below it has area (120/360)·π·1² = π/3. The isosceles triangle formed by the two radii and the base has area ½·1·1·sin120° = √3/4. The shaded segment is the sector minus this triangle, i.e. π/3 − √3/4. The other options use incorrect triangle areas (1/2, 3/4, 1). Hence the answer is π/3 − √3/4.