Find the area of a shaded region in the figure, where a circular arc of radius 7cm has been drawn with vertex A of an equilateral triangle ABC of side 14cm as centre.

Explanation

Given : side of equilateral triangle = 14 cm and radius of circular arc = 7cm

Area of equilateral `/_\ ABC = (sqrt3)/4 xx (side)^2 `

Area of equilateral `/_\ ABC = (sqrt3)/4 xx (14)^2 = 84.87 cm^2`

Area of circle =` pi xx r^2`

Area of circle = `(22/7) xx 7^2 =154 cm`

`/_A = 60^0` ( `/_\ ABC` is an equilateral triangle)

Area of sector = `( theta / 360^0) xx pi xx r^2`

Area of sector = `(60^0/360^0) xx (22/7) xx 7^2 = 25.66 `

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