How is geometry used in Track & Field?

Running tracks are oval in shape. They are made this way on purpose.

Step-by-step explanation:

If you are running a short race, such as a 100m sprint, it is convenient and sensible to run this in a straight line. You could also run a 200m or 400m race in a straight line, but the required track would be a very long. It would be inconvenient. It would be a poor spectator sport. It would be awkward in logistics moving from one end to the other end when not racing. It would not be the best use of space and would make a poor arena.

They can use it figure out how big the track needs to be to fit their specific needs