In figure arcs are drawn by taking vertices A, B and C of an equilateral triangle of side 10 cm, to intersect the sides BC, CA and AB at their respective mid-points D, E and F. Find the area of the shaded region. (use π = 3.14)


Since D, E, F bisects BC, CA, AB respectively.


AE = EC = CD = DB = BF = FA = 5 cm


Now area of the shaded region = (Area of the three sectors)


Since the triangle is an equilateral triangle, therefore each angle is of 60°


Angle subtended at the center of each sector = 60°


Angle subtended at the center (in radians) = θ = 62π/180 = π/3


Radius of each sector = 5 cm


Area of a sector of a circle




Area of three sectors of a circle


= 78.5/2 cm2


= 39.25 cm2


Area of shaded region = 39.25 cm2


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