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ABCD is rectangle, having AB = 20 cm and BC = 14 cm. Two sectors of 180° have been cut off. Calculate: (i) the area of the shaded region. (ii) the length of the boundary of the shaded region.

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If you open math book you will find a lot of mathematical
questions but you should have solve this question.
It is from class 10 rd sharma chapter 15.4 mensuration .

In this question we have to find the the area of the shaded
region and the length of the boundary of the shaded region
given that ABCD is rectangle, having AB = 20 cm and BC = 14 cm.
Two sectors of 180° have been cut off.

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1. Given,

Length of the rectangle = AB = 20 cm

Breadth of the rectangle = BC = 14 cm

(i) Area of the shaded region = Area of rectangle – 2 x Area of the semi-circle

= l x b – 2 x ½ πr2

= 20 x 14 – (22/7) x 72

= 280 – 154

= l26 cm2

(ii) Length of the boundary of the shaded region = 2 x AB + 2 x circumference of a semi-circle

= 2 x 20 + 2 x πr

= 40 + 2 x (22/7) x 7

= 40 + 44

= 84 cm

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