An oval track is made by erecting semicircles on each end of a 60m by 120m rectangle. Find the length of the track and the area enclosed by the track

Refer to the figure shown below.

Because the question states that the semi circles are at the ends of the rectangle, each semicircle has a radius of 30 m.

The circumference of the oval is

2π (30) + 2*120 = 60π + 240 m = 428.5 m

The area of the oval is

π (30²) + 60*120 = 900π + 7200 m² = 1.0027 x 10⁴ m²

Note:

If the semi circles are placed on the 120-m sides of the rectangle, then similar calculations yield:

Circumference = 120π + 120 m = 497 m

Area = 3600π + 7200 m² = 1.851 x 10⁴ m²

Answer:

If the semi circles are placed on the 60-m sides of the rectangle, then

Circumference = 60π + 240 m, or 428.5 m

Area = 900π + 7200 m², or 1.0027 x 10⁴ m²

if the semi circles are placed on the 120-m sides of the rectangle, then

Circumference = 120π + 120 m, or 497 m

Area = 3600π + 7500 m², or 1.851 x 10⁴ m²