Check sibling questions

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.

Slide62.JPG

Slide63.JPG

 

This video is only available for Teachoo black users

 

Get live Maths 1-on-1 Classs - Class 6 to 12


Transcript

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

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

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.