Question

In the following figure, the inside perimeter of a practice running track with semi-circular ends and straight parallel sides is 312 m. The length of the straight portion of the track has a uniform width of 2 m through out, find its area.

Answer 1

Given: Inside perimeter P = 312 m, uniform track width w = 2 m.

Step-wise calculation:

1. When a closed curve is offset outward by distance w, the area added equals P × w + πw² (outer area – inner area = perimeter × width + area of a circle of radius w).

2. So, area of the track

= P × w + πw² 

= 312 × 2 + π × 2² 

= 624 + 4π

3. Using `π = 22/7`

Area = `624 + 4 xx 22/7`

= `624 + 88/7`

= `4456/7` m²

= 636.5714 m²

Area of the track

= `4456/7` m²

= `636 4/7` m²

= 636.57 m²