Given:
The width of the rectangle is 9 yd.
Required:
To find the area of the shaded region.
Explanation:
From the given figure,
Width of the rectangle is 9 yd.
Therefore, the radius of the semicircle is 9yd.
And the length of the rectangle is diameter of the semicircle.
[tex]\begin{gathered} =2\times9 \\ =18yd \end{gathered}[/tex]
Now, the area of the rectangle is,
[tex]\begin{gathered} A=L\times W \\ =9\times18 \\ =162yd^2 \end{gathered}[/tex]
Now the area of the semicircle is,
[tex]\begin{gathered} A=\frac{\pi r^2}{2} \\ =\frac{3.14\times9^2}{2} \\ =\frac{254.34}{2} \\ =127.17yd^2 \end{gathered}[/tex]
Now the area of the shaded region = Area of the rectangle - Area of the semicircle.
[tex]\begin{gathered} =162-127.17 \\ =34.83\text{ yd}^2 \end{gathered}[/tex]
Final Answer:
The area of the shaded region is 34.83 yd square.
