In Figure, ABC  is an equilateral triangle of side 8cm. A, B and C are the centres of circular arcs of radius 4cm. Find the area of the shaded region correct upto 2 decimal places.

Explanation

Given : side of equilateral triangle `a =8cm` and radius of circular arcs `r=4cm`

Area of equilateral triangle `= (sqrt3)/4 xx a^2`

`:.`Area of equilateral triangle `= (sqrt3)/4 xx (8^2) = 27.71`

`theta = 60^0 `(triangle is equilateral )

Area of circular arc`= (theta/360) xx pi xx r^2 `

Area of circular arc`= (60/360) xx (22/7) xx 4^2 = 8.38 cm^2 `

`:.` Area of circular 3 arcs `=3 xx 8.38 = 25.14 cm^2`

Area of the shaded region= Area of equilateral triangle - Area of circular 3 arcs

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