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)

Question

Philoid · Accepted Answer

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