RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 18. Area of Circle, Sector and Segment

Subject: Maths - Class 10th

Q. No. 35 of Exercise 18A

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35

Find the perimeter of shaded region in the figure, if ABCD is a square of side 14 cm and APB and CPD are semicircles.

Given:

Side of square = 14 cm


Diameter of semi circle = 14 cm


Radius of semi circle = = 7 cm


There are 2 semi circles of same radius.


We consider it as one circle with radius 7 cm.


So,


Perimeter of 2 semicircles = Perimeter of circle = 2πr


= 2 × × 7


= 2 × 22 = 44 cm


Perimeter of shaded region = Perimeter of 2 semicircles + 2 × Side of Square = 44 + 2 × 14 = 44 + 28 = 72 cm


Hence, the area of the shaded region is 72 cm.


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