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Question
In the given figure, arcs have been drawn of radius 7 cm each with vertices A, B, C and D of quadrilateral ABCD as centres. Find the area of the shaded region.
Solution
Let the measure of ∠A, ∠B, ∠C and ∠D be θ1, θ2, θ3 and θ4 respectively
Required area = Area of sector with centre A + Area of sector with centre B + Area of sector with centre C + Area of sector with centre D
= `θ_1/360 xx π xx 7^2 + θ_2/360 xx π xx 7^2 + θ_3/360 xx π xx 7^2 + θ_4/360 xx π xx 7^2`
= `((π_1 + π_2 + π_3 + π_4))/360 xx pi xx 7^2`
= `((360))/360 xx 22/7 xx 7 xx 7` ......(By angle sum property of a triangle)
= 154 cm2
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