# Mensuration-33

The inside perimeter of a running track is 400 m. The length of each of the straight portion is 90 m
and the ends are semi-circles. If the track is everywhere 1.4 m wide, find the area of the track. Also, find
the length of the outer running track.

Solution: Inside perimeter of the track = 400 m

Total length of the two portions = 2 x 90 = 180 m

Therefore, the length of the remaining portions = 400 - 180 = 220 m

Circumference of the remaining semi-circular portions

= Π r + Π r = 2 Π r, where r is the radius.

2 Π r = 220; => 2 x 22 / 7 x r = 220

=> r = 220 x 1/2 x 7/22 = 35 m

Therefore, Radius of the circular portion of the outer running track = 35 m + 1.4 m = 36.4 m

Area of the track = area of the two rectangles of dimensions 90 m x 1.4 m + area of the circular rings

= 2 x 90 x 1.4 + 22/7 [(36.4)2 - (35)2]

= 252+ 22/7 x (36.4 + 35) (36.4 - 35)

= 252 + 22/7 x 71.4 x 1.4 = 252 + 314.16 = 566.16 cm2

Length of the outer running track = 2 x 90 + 2 x 22/7 x 36.4 = 180 + 228.8 = 408.8 m