With vertices A, B and C of ΔABC as centres, arcs are drawn with radii 14 cm and the three portions of the triangle so obtained are removed. Find the total area removed from the triangle.

With vertices A, B and C of ΔABC as centres, arcs are drawn with radii - CBSE Class 10 Sample Paper for 2024 Boards - Maths Standard

part 2 - Question 25 (Choice 1) - CBSE Class 10 Sample Paper for 2024 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards - Class 10
part 3 - Question 25 (Choice 1) - CBSE Class 10 Sample Paper for 2024 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards - Class 10

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Total area removed from the triangle = Area of sector at point A + Area of sector at point B + Area of sector at point C Area of Sector We know that Area of sector = 𝜃/(360°) × πr2 and radius = 14 cm Thus, Area of Sector at point A = (∠𝐴)/(360°) × πr2 Area of Sector at point B = (∠𝐵)/(360°) × πr2 Area of Sector at point C = (∠𝐶)/(360°) × πr2 Therefore, Total area removed from the triangle = (∠𝐴)/(360°) × πr2 + (∠𝐵)/(360°) × πr2 + (∠𝐶)/(360°) × πr2 = 𝟏/(𝟑𝟔𝟎°) × πr2 (∠ A + ∠ B + ∠ C) Since sum of angles of a triangle = 180° = 1/(360°) × πr2 × 180° = 𝟏/𝟐 × πr2 Putting r = 14cm = 1/2 × 22/7 × (14)2 = 11/7 × 14 × 14 = 11 × 28 = 308 〖𝒄𝒎〗^𝟐

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