In the given figure, arcs have been drawn of radius 7cm each with vertices A, B, C and D of quadrilateral ABCD as centres. Find the area of the shaded region.

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Question 24 (Choice 2) In the given figure, arcs have been drawn of radius 7cm each with vertices A, B, C and D of quadrilateral ABCD as centres. Find the area of the shaded region.Given Radius of arc = r = 7 cm Now, Area of the shaded region = Area of sector at point A + Area of sector at point B + Area of sector at point C + Area of sector at point D = (∠ 𝐴)/(360°) × 𝜋𝑟^2+(∠ 𝐵)/(360°) " × " 𝜋𝑟^2+(∠ 𝐶)/(360°) " × " 𝜋𝑟^2+(∠ 𝐷)/(360°) " × " 𝜋𝑟^2 = 1/(360°) × 𝜋𝑟^2 (∠ 𝐴+∠ 𝐵+∠ 𝐶+∠ 𝐷) Since ABCD is a quadrilateral Sum of angles = 360° ∴ ∠ 𝐴+∠ 𝐵+∠ 𝐶+∠ 𝐷 = 360° = 1/(360°) × 𝜋𝑟^2 × 𝟑𝟔𝟎° = 𝜋𝑟^2 Putting r = 7 cm = 22/7 × 7^2 = 22 × 7 = 154 cm2

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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.