Final answer:
None of the given options accurately represent the area enclosed by the figure. The correct total area calculation is the sum of the area of the square and the areas of the circles: 2500m² + π(25m)^2.
Step-by-step explanation:
The question asks for the equation to find the area enclosed by a figure made by attaching semicircles to each side of a 50m by 50m square. To calculate this, first find the area of the square, and then add the area of the four semicircles, which together form two full circles with a diameter of 50m each.
The area of the square is 50m × 50m = 2500m². The radius of each semicircle is 25m (since the diameter is 50m), so the area of a full circle would be π × (25m)². Therefore, the area of two full circles would be 2 × π × (25m)², which simplifies to 2π(50m)^2 / 4. Simplified further, it becomes 0.5π(50m)^2.
Adding the area of the square and the circles gives us the total area: 2500m² + 0.5π(50m)^2. This is equivalent to 2500m² + π(25m)^2, which when you compute using the value of π, will give you the area in square meters. Thus, the correct equation for the area enclosed by this figure is 2500m² + π(25m)^2. None of the options provided in the question exactly match this equation.