Final answer:
The total area of the training field, which is composed of a rectangle and two semicircles, is calculated to be 11817.6 square meters.
Step-by-step explanation:
The question deals with the calculation of the area of a training field composed of a rectangle and two semicircles. The steps involve finding the area of the rectangle using the formula (length × width) and then calculating the area of the semicircles using the formula πr² (where r is radius) divided by 2, since a semicircle is half of a circle. For the rectangle with the given dimensions 96 m × 76 m, the area will be:
Rectangle area = 96 m × 76 m = 7296 m².
The diameter of each semicircle is equal to the width of the rectangle, which is 76 m, so the radius (r) is half of that, 38 m. The area of one semicircle will be:
Semicircle area = (π × (38 m)²) / 2 = (π × 1444 m²) / 2 = 2260.8 m² (using π to its approximate value of 3.1416).
Since there are two semicircles,
Total area of semicircles = 2 × 2260.8 m² = 4521.6 m².
The total area of the training field is the sum of the areas of the rectangle and the semicircles:
Total area of training field = 7296 m² + 4521.6 m² = 11817.6 m².