Question

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).

Answer 1

Since, ΔABC is an equilateral triangle.

∴ ∠A = ∠B = ∠C = 60°

And AB = BC = CA = 10 cm

E, F and D are mid-points of the given sides.

∴ AE = EC = CD = DB = BF = FA = 5 cm

Radius of a sector (r) = 5 cm

Now, area of sector CDE

= `θ/360^circ xx π"r"^2`

= `60^circ/360^circ xx 3.14 xx (5)^2 "cm"^2`

= `(3.14 xx 25)/6 "cm"^2`

= `78.5/6 "cm"^2`

= 13.0833 cm²

∴ Area of shaded region

= 3 (Area of sector CDE)

= 3 × 13.0833 cm²

= 39.25 cm²