An athletic track 14 m wide consists of two straight sections 120 m long joining semi-circular ends whose inner radius is 35 m. Calculate the area of the track.
We have
OB=35 m and AB=CD=14 m,OA=(35+14) m=49 m
Now, Area of the track = Area of rectangle ABCD +Area of rectangle EFGH + 2{Area of the semi-circle with radius 49m} - 2{ Area of the semi-Circle with radius 35m}
=(AD×AB)+(EH×EF)+2[12π(49)2]−2[12×π(35)2]
=(14×120)+(14×120)+2{12×227×(49)2}−2{12×227×(35)2}
={3360+227(49+35)(49−35)}=7056 m2