We can calculate the shaded area as the difference in the area between the square and the half circle.
The side of the square is 25 ft.
The half circle has radius equal to half the length of the side: r=25/2=12.5 ft.
Then, we can write:
[tex]\begin{gathered} A=A_{sq}-\frac{1}{2}A_c_{} \\ A=a^2-\frac{1}{2}(\pi r^2) \\ A\approx25^2-\frac{1}{2}\cdot3.14\cdot12.5^2 \\ A\approx625-1.57\cdot156.25 \\ A\approx625-245.31 \\ A\approx379.69 \end{gathered}[/tex]
NOTE: Asq is the area of the square and Ac is the area of the circle, multiplied by 1/2 beacuse it is half a circle we have to substract from the square.
Answer: The shaded area is 379.69 square feet.
