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प्रश्न
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).
उत्तर
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
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