CBSE Class 10 Answered

Shaded area = area of quadrilateral ABDE - area of minor sector of 4cm circle, near shaded area - area of minor sector of 12 cm circle, near shaded area.

AB = 4 + 12 = 16 cm.

AC  BD

AE = CD = 4 cm

BC = BD - CD = 12 - 4 = 8 cm

cos B = BC/AB = 8/16 = 1/2

B = 60

Area of minor sector in 12 cm circle, near shaded area = (1/2)(π/3)(12)(12) = 24π

In quadrilateral ABDE, E = D = 90, B = 60 and hence A = 30.

Area of minor sector in 4 cm circle, near shaded area =  (1/2)(π/6)(4)(4) = 4π/3

Area of quadrilateral, ABDE = Area of rectangle ACDE + Area of triangle ABC

= (AC)(AE) + (1/2)(AC)(BC)

= 83x4 + 0.5x83 x8 = 643       ...........AC = (AB²-BC²) 

The shaded area = 643 - 4π/3  - 24π = 31.3 cm²

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