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).
ABC is an equilateral triangle.
And, AB = BC = CA = 10 cm
As, D, E, F are mid-points of the sides,
AE = EC = CD = BD = BF = FA = 5 cm
∠A = ∠B = ∠C = 60°
Area of sector CDE = `theta/360 xx pir^2`
= `60/360 xx pi (5)^2`
= 13.0833 cm2
Area of shaded region = 3 × Area of sector CDE
= 3× 13.0833
= 39.25 cm2
Concept: Areas of Combinations of Plane Figures
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