Solution:
Given the a figure;
The figure is a square with the unshaded region is a semi circle.
The measure of the side lengths of the square is 25 ft
To find the area, A, of the shaded region, the formula is
[tex]\begin{gathered} A=Area\text{ of Square}-Area\text{ of a semi circle} \\ A=(l^2)-(\frac{\pi r^2}{2}) \end{gathered}[/tex]
Where
[tex]\begin{gathered} l=25\text{ ft} \\ d\text{ is the diameter of the semi circle} \\ d=l=25\text{ ft} \\ r\text{ is the radius of the semi circle} \\ r=\frac{d}{2}=\frac{25}{2}=12.5\text{ ft} \\ r=12.5\text{ ft} \end{gathered}[/tex]
Substitute the values of the variables into the formula above
[tex]\begin{gathered} A=25^2-(\frac{\pi\cdot12.5^2}{2}) \\ A=625-245.4369 \\ A=379.5631\text{ ft}^2 \\ A=379.56\text{ ft}^2\text{ \lparen nearest hundredth\rparen} \end{gathered}[/tex]
Hence, the answer is 379.56 ft² (nearest hundredth)
