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.

Answer 1

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