Final answer:
The area of the window is calculated by adding the area of a square to the area of a semi-circle. The square area is x², and the semi-circle, which is half of a full circle with radius x/2, has an area of (π/8)x². Summing these gives (1 + π/8)x², which isn't listed in the provided options.
Step-by-step explanation:
To determine the area of a window that comprises a square with sides of length x inches and a semi-circle with a diameter of x inches, we need to add the area of the square and the area of the semi-circle.
The area of the square is easy to calculate: Area of square = x².
To calculate the area of the semi-circle, first, we determine the area of a full circle of diameter x, which will have a radius (r) of x/2. Using the formula for the area of a circle (A=πr²), we obtain Area of full circle = π(x/2)². Simplified, this gives us (π/4)x² for the full circle. However, since we are only dealing with a semi-circle, we take half of this area, resulting in (π/8)x².
Finally, we combine the areas of the square and the semi-circle: x² + (π/8)x², which simplifies to (1 + π/8)x².
While the options provided (A, B, C, D) do not match the correct area calculation, they seem to suggest adding the area of the square with portions of the circle's area. The correct answer should reflect the area of the square plus half the area of the circle as detailed in our calculation.