Question 25 (Choice 1) - CBSE Class 10 Sample Paper for 2024 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards
Last updated at Dec. 13, 2024 by Teachoo
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.
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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
Made by
Davneet Singh
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo
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