Question

The adjoining sketch shows a running tract $3.5m$ wide all around which of two straight paths and two semicircular rings. Find the area of the track.

Answer 1

Given that,

Length of one side of the track $l=140m$

Width of the track $b=3.5m$

Radius of the semicircular track $=\frac{42}{2}=21m$

We know that,

$\therefore$ Area of the track $=2\times$Area of straight paths$+2\times$Area if semicircular paths

$=2\times l\times b+2\times \frac{\pi (R^2-r^2)}{2}$

$=2\times 140\times 3.5+2\times \frac{22\times ({24.5}^2-{21}^2)}{7\times 2}$

$=980+500.5$

$=1480.5m^2$

Then,

We get area of the tack is $2366m^2$.