85. Find the area of thesegment AYB shown inthe given figure. If radiu

1.	85. Find the area of thesegment AYB shown inthe given figure. If radius Aof the circle is 21 cm and 7ZAOB 120Â°120
Answer» In ∆AOB, draw a perpendicular line from O which intersect AB at M. In ∆AOM, angle AMO = 90angle OAM = 30cos 30 = AM/AO√3/2 = AM/21AM = 21×√3/2AB = 2(AM)=2(21×√3/2)=21√3 OM^2 = AO^2-AM^2=21^2-(21√3/2)^2=441-330.51=110.48OM =√110.48OM =10.51 OM = 10.51cm Area of ∆AOM = 1/2 AB × OM=1/2 ×21√3 ×10.51=191.14cm^2 Area of sector AOBY = 120πr^2/360=120×21×21×22/2520=462cm^2 Area of segment AYB = Area of sector OAYB -Area of∆OAB=462-191.14=270.86 Area of segment AYB is 270.86cm^2.

85. Find the area of thesegment AYB shown inthe given figure. If radius Aof the circle is 21 cm and 7ZAOB 120Â°120

Answer»

In ∆AOB, draw a perpendicular line from O which intersect AB at M.

In ∆AOM, angle AMO = 90angle OAM = 30cos 30 = AM/AO√3/2 = AM/21AM = 21×√3/2AB = 2(AM)=2(21×√3/2)=21√3

OM^2 = AO^2-AM^2=21^2-(21√3/2)^2=441-330.51=110.48OM =√110.48OM =10.51

OM = 10.51cm

Area of ∆AOM = 1/2 AB × OM=1/2 ×21√3 ×10.51=191.14cm^2

Area of sector AOBY = 120πr^2/360=120×21×21×22/2520=462cm^2

Area of segment AYB = Area of sector OAYB -Area of∆OAB=462-191.14=270.86

Area of segment AYB is 270.86cm^2.