Question
Three circles, each having radius equal to 4 cm, are
drawn with the vertices of an equilateral triangle as the centres. If the length of each side of the triangle is equal to 8 cm, then what is the area (in cm2) of the portion of the triangle that is NOT covered by the sectors of the circles?Solution
Area of the triangle = β3/4 Γ 82 = 16β3 cm2 Total area of the sectors of the circles that are lying on the triangle = 3 Γ 60/360 Γ Ο Γ 42 = 8Ο cm2 Hence, required area = 16β3 - 8Ο = 8 (2β3 - Ο) cm2
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