Final answer:
To find the area of the training field consisting of a rectangle and two semicircles, calculate the area of the rectangle (80 m × 60 m = 4800 m²) and the combined area of the semicircles (which forms a full circle with a radius of 30 m, thus 2827.43 m²). Sum them to get 7627.43 m².
Step-by-step explanation:
The training field is made up of a rectangle and two semicircles on the shorter sides of the rectangle. To find the area of the training field, we first calculate the area of the rectangle which is length × width. In this case, it's 80 m × 60 m = 4800 m². Next, we find the area of the two semicircles which, when combined, make a full circle with a diameter equal to the width of the rectangle, so the radius (r) is 30 m. The area of a circle is πr², so for one full circle it is π × 30² m² = π × 900 m². Therefore, the area of the two semicircles together, which form one full circle, is 3.1416 × 900 m² = 2827.43 m² (approx).
Now we sum the area of the rectangle and the area of the full circle to get the total area of the training field: 4800 m² + 2827.43 m² = 7627.43 m² (approximately). However, none of the provided options match this result, which suggests there might be an error in the question or the options given. If we consider the options provided, we might assume the calculation should consider the entire width of the rectangle including the semicircles (which would make the rectangle actually the midsection of a larger circle with an 80 m diameter). In this case, the semicircles' diameter would be 60 m, and the radius of the combined circle would be 30 m, leading to a full circle's area of 2827.43 m² and when summed with the rectangle's 4800 m² we get the total area as 7627.43 m². Since none of the options match, the student should check the question for accuracy.