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

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

Answers (1)

39.25 cm2

Solution

Angle made by vertices A, B and C = 60°     { In equilateral triangle all angles = 60°}

Diameter of circle = 10

Radius =\frac{10}{2}=5 cm

Area of shaded region = 3 × Area of sector       

                                    \\=3 \times \frac{\pi r ^{2} \theta}{360}\\ =\frac{3 \times (5)^{2} \times 3.14 \times 60 }{360}\\ =\frac{25 \times 3.14}{2}\\ =\frac{25 \times 314}{2 \times 100}\\ =\frac{25 \times 157}{100}\\ =39.25 cm^{2}

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