Area of combination of figures - two circles, circle and square

Chapter 9 Class 7 Perimeter and Area
Concept wise

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Ex 9.2, 10 From a circular card sheet of radius 14 cm, two circles of radius 3.5 cm and a rectangle of length 3 cm and breadth 1cm are removed. (as shown in the adjoining figure). Find the area of the remaining sheet. (ππππ π=22/7) Remaining Area = Area of larger circle β 2 Γ Area of smaller circle β Area of rectangle Area of larger circle Radius of larger circle = R = 14 cm Area of larger circle = πR2 = 22/7 Γ (14)2 = 22/7 Γ 14 Γ 14 = 22/1 Γ 2 Γ 14 = 44 Γ 14 = 616 cm2 Area of smaller circle Radius of larger circle = r = 3.5 cm Area of smaller circle = πr2 = 22/7 Γ (3.5)2 = 22/7 Γ (35/10)^2 = 22/1 Γ (7/2)^2 = 22/7 Γ 7/2 Γ 7/2 = 11/7 Γ 7/1 Γ 7/2 = 22/7 Γ 1 Γ 7/2 = 77/2 = 38.5 cm2 Area of rectangle Length of rectangle = l = 3 cm Breadth of rectangle = b = 1 cm Area of rectangle = l Γ b = 3 Γ 1 = 3 cm2 Therefore, β΄ Remaining Area = Area of larger circle β 2 Γ Area of smaller circle β Area of rectangle = 616 β 2 Γ (77/2) β 3 = 616 β 77 β 3 = 616 β 80 = 536 cm2 β΄ Required area is 536 cm2