RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 18. Area of Circle, Sector and Segment

Subject: Maths - Class 10th

Q. No. 31 of Exercise 18A

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31

In the given figure, find the area of the shaded region, if ABCD is a square of side 14 cm and APD and BPC are semicircle.

Given:

Side of square = 14 cm


Diameter of each semicircle = 14 cm


Radius of each semicircle = = 7 cm


Both the semicircles have same radius.


We consider one circle of radius 7 cm.


Area of shaded region = Area of square – Area of circle ….……. (i)


Area of square = side × side


= 14 × 14 = 196 cm2


Area of circle = πr2


= × 7 × 7 = 22 × 7 = 154 cm2


Thus, using (i), we have


Area of shaded region = 196 – 154 = 42 cm2


Hence, the area of shaded region is 42 cm2.


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