Check sibling questions

Example 6 - Find area of shaded design, ABCD is a square 10 cm - Examples

Example 6 - Chapter 12 Class 10 Areas related to Circles - Part 2
Example 6 - Chapter 12 Class 10 Areas related to Circles - Part 3
Example 6 - Chapter 12 Class 10 Areas related to Circles - Part 4

This video is only available for Teachoo black users

Example 6 - Chapter 12 Class 10 Areas related to Circles - Part 5
Example 6 - Chapter 12 Class 10 Areas related to Circles - Part 6
Example 6 - Chapter 12 Class 10 Areas related to Circles - Part 7

This video is only available for Teachoo black users

 

Solve all your doubts with Teachoo Black (new monthly pack available now!)


Transcript

Example 6 (Method 1) Find the area of the shaded design in figure, where ABCD is a square of side 10 cm and semicircles are drawn with each side of the square as diameter. (Use π= 3.14) Given Side of square ABCD = 10 cm Area of square ABCD = (side)2 = (10)2 = 100 cm2 Given semicircle is drawn with side of square as diameter, So, Diameter of semicircle = Side of square = 10 cm Radius of semicircle = 𝑠𝑖𝑑𝑒/2 = 10/2 = 5 cm Area of semi circle AD = 1/2× area of circle = 1/2×πr2 = 1/2×π×(5)2 = (3.14 × 25)/2 Since radius is same for semi-circle AD, BC, AB, CD Area of semi circle AD = Area of semi circle BC = Area of semi circle AB = Area of semi circle CD = (3.14 × 25)/2 Let us mark the unshaded region as I , II, III, and IV. Area of shaded region = Area of ABCD – (Area of I + II + III + IV) Area of region I + Area of region III = Area of square ABCD – (Area of semicircle AD + area of semi circle BC) Area of region II + Area of region IV = Area of square ABCD – (Area of semicircle AB + area of semi circle CD) So, Area of region (I + II + III + IV) = 2(Area of square ABCD) – (Area of semicircle AD + BC + AB + CD) Putting values = 2(100) – ((3.14 × 25)/2 + (3.14 × 25)/2 + (3.14 × 25)/2 + (3.14 × 25)/2) = 200 – 4 × (3.14 × 25)/2 = 200 – 2 × 3.14 × 25 = 200 – 157 = 43 cm2 Now, Area of shaded region = Area of ABCD – (Area of I + II + III + IV) = 100 – 43 = 57 cm2 Hence, area of shaded region = 57 cm2 Example 6 (Method 2) Find the area of the shaded design in figure, where ABCD is a square of side 10 cm and semicircles are drawn with each side of the square as diameter. (Use π= 3.14) Given Side of square ABCD = 10 cm Area of square ABCD = (side)2 = (10)2 = 100 cm2 Given semicircle is drawn with side of square as diameter, So, Diameter of semicircle = Side of square = 10 cm Radius of semicircle = 𝑠𝑖𝑑𝑒/2 = 10/2 = 5 cm Area of semi circle AD = 1/2× area of circle = 1/2×πr2 = 1/2×π×(5)2 = (3.14 × 25)/2 Since radius is same for semi-circle AD, BC, AB, CD Area of semi circle AD = Area of semi circle BC = Area of semi circle AB = Area of semi circle CD = (3.14 × 25)/2 Area of 4 semicircles – Area of shaded region = Area of square ABCD Area of shaded region = Area of 4 semicircles – Area of square ABCD Area of shaded region = 4 × (3.14 × 25)/2 – 100 = 2 × 3.14 × 25 – 100 = 157 – 100 = 57 cm2

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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.