Calculate the area of the designed region in figure, common between the two quadrants of circles of radius 8cm each.
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Solution
i) Area of Square ABCD =a2=(8)2=64cm2 ii) Sum of Areas of Part II and Part III: = Area of segment with centre D and radius of 8cm ∴=θ360×πr2 =90360×227×(8)2 =14×227×64 =3527sq.cm iii) Area of part I: =(Sum of Part I, II and III)-(Sum of area of Part II, III) = Area of Square ABCD− (Sum of area of Part II and III) =64cm2−3527cm2 =448−3527cm2 =967cm2 Similarly, Area of Part II=967cm2 ∴ Area of Region III =3527−967 =2567cm2