Question

A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 85m long and 57m wide. What is the length of a training track running around the field? Do not round any intermediate computations. Round your final answer to the nearest hundredth and be sure to include the correct unit. If necessary, refer to the list of geometry formulas.

Answer 1

463.52 meters

Explanation:

To find the length of the training track running around the field, we need to calculate the perimeter of the entire field.

The field is made up of a rectangle with dimensions 85m by 57m, and two semicircles with a radius of 57/2 = 28.5m.

The perimeter of the rectangle is 2(85m) + 2(57m) = 284m.

The perimeter of each semicircle is half the circumference of a full circle with radius 28.5m, which is π(28.5m) = 89.76m. So the total perimeter of both semicircles is 2(89.76m) = 179.52m.

Therefore, the total perimeter of the field is 284m + 179.52m = 463.52m.

Rounding to the nearest hundredth, the length of the training track running around the field is 463.52 meters.