The inside perimeter of a running track shown in the figure is 400 m. The length of each of the straight portions is 90 m, and the ends are semicircles. If the track is 14 m wide everywhere, find the area of the track. Also, find the length of the outer boundary of the track.

Consider the figure as a combination of two semicircles on the ends of the rectangle


Let the length of rectangle be ‘L’ m and breadth be ‘B’ cm


Given L = 90 m, W = 14 m


Perimeter of running track = 400 m


Perimeter of inside of running track = 2L + Arc of two semicircles eqn1


Arc length of a semicircle = πr where r = radius


400 = (2×90) + (2×πr) (putting values in eqn1)


400 = 180 + 2πr


400 – 180 = 2πr


220 = 2πr





r = 35 m


Area of inner of running track = Area of rectangle + 2×area of semicircles eqn2


Area of rectangle = L×B


Here B = 2r


B = 70 m


Area of inner rectangle = 90×70


Area of inner rectangle = 6300 m2 eqn3




Area of inner semicircles = 1225π



Area of inner semicircle = 175×22


Area of inner semicircle = 3850 m2 eqn4


Area of inner of running track = 6300 + 3850 (from3&4)


Area of inner of running track = 10150 m2


Now radius of semicircles of outer of the running track = R = r + W


R = 35 + 14


R = 49 m




Area of outer semicircles = 2401π



Area of outer semicircles = 343×22


Area of outer semicircle = 7546 m2 eqn5


Breadth of outer running track = B’ = 2R


B’ = 2×49


B’ = 98 m


Area of outer rectangle = L×B’


Area of outer rectangle = 90×98


Area of outer rectangle = 8820 m2 eqn6


Area of entire ground = 8820 + 7546 (from 5&6)


Area of entire ground = 16366 m2


Area of running track = Area of entire ground – Area of inner ground


Area of running track = 16366 – 10150


Area of running track = 6216 m2


Perimeter of outer boundary = 2L + Arc of outer semicircles


Arc length of an outer semicircle = πR, where R = outer radius



Perimeter of outer boundary = 180 + (2×22×7)


Perimeter of outer boundary = 180 + 308


Perimeter of outer boundary = 488 m


Area of running track is 6216 m2 and perimeter of outer boundary is 488 m.


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