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

From figure,

Length of inner rectangle ABCD = 140 m

Breadth of inner rectangle ABCD = 42 m

Diameter of inner semi-circle = 42 m

Radius of inner semi-circle (r) = $\dfrac{42}{2}$ = 21 m.

Length of outer rectangle = Length of inner rectangle = 140 m

Breadth of outer rectangle = Breadth of inner rectangle + 2 × Width of outer track = 42 + 2 × 3.5 = 42 + 7 = 49 m.

Diameter of outer semi-circle = 49 m

Radius of outer semi-circle (R) = $\dfrac{49}{2}$ = 24.5 m.

Area of track = Area of outer rectangle - Area of inner rectangle + 2(Area of outer semi-circle - Area of inner semi-circle)

$= 140 × 49 - 140 × 42 + 2(\dfrac{πR^2}{2} - \dfrac{πr^2}{2}) \\[1em] = 140(49 - 42) + 2π \times \dfrac{1}{2}(R^2 - r^2) \\[1em] = 140 × 7 + π[(24.5)^2 - (21)^2] \\[1em] = 980 + π[600.25 - 441] \\[1em] = 980 + \dfrac{22}{7} \times 159.25 \\[1em] = 980 + 500.5 \\[1em] = 1480.5 \text{ m}^2.$

Hence, area of track = 1480.5 m².