Question
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 = 22/7 and √3 = 1.73).Solution
Given: Side of equilateral triangle = 28 cm
Radius of each circle = 14 cm (half of 28 cm)
π = 22/7, √3 = 1.73 Area of triangle = (√3 / 4) × a²
= (1.73 / 4) × 28² = 1.73 × 196 = 339.08 cm² Area of one sector = (60/360) × π × r²
= (1/6) × (22/7) × 14² = (1/6) × (22/7) × 196 ≈ 102.67 cm²
Total area of 3 sectors = 3 × 102.67 = 308.01 cm² Required area = 339.08 − 308.01 = 31.07 cm²
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