Last updated at Aug. 5, 2021 by Teachoo

Transcript

Example 3 Find the area of the segment AYB shown in figure, if radius of the circle is 21 cm and โ AOB = 120ยฐ. (Use ฯ = 22/7 ). In a given circle, Radius (r) = 21 cm And, ๐ = 120ยฐ Area of segment AYB = Area of sector OAYB โ Area of ฮOAB Area of sector OAYB = ๐/360ร๐๐2 = 120/360ร22/7ร(21)2 = 1/3ร22/7ร21ร21 = 22 ร 21 = 462 cm2 Finding area of ฮ AOB Area ฮ AOB = 1/2 ร Base ร Height We draw OM โฅ AB โด โ OMB = โ OMA = 90ยฐ In ฮ OMA & ฮ OMB โ OMA = โ OMB OA = OB OM = OM โด ฮ OMA โ ฮ OMB โ โ AOM = โ BOM โด โ AOM = โ BOM = 1/2 โ BOA Also, since ฮ OMB โ ฮ OMA โด BM = AM โ BM = AM = 1/2 AB From (1) AM = 1/2AB 2AM = AB AB = 2AM Putting value of AM AB = 2 ร โ3/2 ร 21 AB = โ3 ร 21 AB = 21โ3 Now, Area of ฮ AOB = 1/2 ร Base ร Height = 1/2 ร AB ร OM = 1/2 ร 21โ3 ร 21/2 = (441โ3)/4 Area of the segment AYB = Area of sector โ area of โ ๐ด๐๐ต = (462 โ 441/4 โ3 ) cm2

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.