CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard

Class 10
Solutions of Sample Papers for Class 10 Boards

## 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.

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Note : This is similar to Example 6 of NCERT β Chapter 12 Class 10

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### Transcript

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 = ππππ/2 = 14/2 = 7 cm Area of semi circle AD = 1/2Γ area of circle = 1/2ΓΟr2 = 1/2Γ22/7 Γ (7)2 = 11 Γ 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 β (Area of semicircle AD + area of semi circle BC) Area of region II + Area of region IV = Area of square ABCD β (Area of semicircle AB + area of semi circle CD) So, Area of region (I + II + III + IV) = 2(Area of square ABCD) β (Area of semicircle AD + BC + AB + CD) Putting values = 2(196) β (77 + 77 + 77 + 77) = 200 β 4 Γ 77 = 392 β 308 = 84 cm2

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#### Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.