Question 29 In the figure, ABCD is a square of side 14 cm. Semi-circles are drawn with each side of square as diameter. Find the area of the shaded region.
First, let us find Area of Square
Given
Side of square ABCD = 14 cm
Area of square ABCD = (Side)2
= (14)2
= 196 cm2
Let us mark the shaded region as I , II, III, and IV.
Also,
Diameter of semicircle = Side of square = 14 cm
Radius of semicircle = 𝑆𝑖𝑑𝑒/2 = 14/2 = 7 cm
Area of semi circle AD = 1/2× area of circle
= 1/2×πr2
= 1/2×22/7 × (7)2
= 11 × 7
= 77 cm2
Since radius is same for semi-circle AD, BC, AB, CD
Area of all semi circles = 77 cm2
Area of region I + Area of region III
= Area of square ABCD
– (Area of semicircle AD + area of semi circle BC)
Area of region II + Area of region IV
= Area of square ABCD
– (Area of semicircle AB + area of semi circle CD)
So, Area of region (I + II + III + IV)
= 2(Area of square ABCD) – (Area of semicircle AD + BC + AB + CD)
Putting values
= 2(196) – (77 + 77 + 77 + 77)
= 200 – 4 × 77
= 392 − 308
= 84 cm2

CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.