Question

The field inside a running track is made up of a rectangle 84.39m (meters) long and 73m (meters) wide, together with a half-circle at each end. The running lanes are 9.76m (meters) wide all the way around. Question: What is the area of the running track that goes around the field? Explain or show your reasoning.

Answer 1

Answer:

3886.53 $m^{2}$

Step-by-step explanation:

The running track consist of two semicircles and a rectangle.

So that;

Diameter of the semicircles = width of the rectangle = 73 m

radius = $\frac{diameter}{2}$

          = $\frac{73}{2}$

          = 36.5 m

But the two semicircles form a circle, so that;

Circumference of a circle = 2$\pi$r

Circumference of the circle formed by the semicircles = 2 x $\frac{22}{7}$ x 36.5

                                          = 229.43 m

Thus,

length of the running track = circumference of the circle formed + length of the two sides of the rectangle

                                             = 229.43 + 84.39 + 84.39

                                             = 398.21 m

The length of the running track is 398.21 m.

Therefore;

Area of the running track = length x width

                                         = 398.21 x 9.76

                                         = 3886.5296

The area of the running track is 3886.53 $m^{2}$.