Question 3
Find the area of the shaded region in figure, where ABCD is a square of side 14 cm.
Area of shaded region = Area of square ABCD – Area of 4 circles
Area of square ABCD
Side of square = 14 cm
Area of square = (side)2
= (14)2
= 14 × 14
= 196 cm2
Area of 4 circles
Since ABCD is a square .
Hence, AB = BC = CD = AD = 14 cm
Now,
Diameter of each circle = 𝐴𝐵/2
= 14/2 = 7 cm
Radius of each circle = 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟/2 = 7/2 cm
Area of one circle = 𝜋𝑟2
= 22/7×(7/2)^2
= 22/7×7/2×7/2
= (11 × 7)/2
= 77/2 cm2
So, Area of 4 circle = 4 × Area of one circle
= 4 × 77/2 cm2 = 154 cm2
Area of shaded region = Area of square ABCD – Area of 4 circles
= 196 – 154
= 42 cm2

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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