A rectangle is placed around a semicircle. The width of the rectangle is 8 yd. We need to find the area of the shaded region, which is the area of the rectangle minus the area of the semicircle. We are given that we should use 3.14 for $\pi$.

1. Problem Description

A rectangle is placed around a semicircle. The width of the rectangle is 8 yd. We need to find the area of the shaded region, which is the area of the rectangle minus the area of the semicircle. We are given that we should use 3.14 for $\pi$.

2. Solution Steps

First, we need to find the dimensions of the rectangle. The width of the rectangle is given as 8 yd. The diameter of the semicircle is also the width of the rectangle, which is 8 yd. Therefore, the length of the rectangle is the diameter of the semicircle, which is 8 yd.

Thus, the rectangle is a square with sides of length 8 yd.

The area of the rectangle is given by:

$Area_{rectangle} = length \times width = 8 \times 8 = 64 \, yd^2$

Next, we need to find the area of the semicircle. The radius of the semicircle is half of the diameter, so the radius $r = \frac{8}{2} = 4$ yd.

The area of a full circle is given by:

$Area_{circle} = \pi r^2$

Since we have a semicircle, its area is half of the area of the full circle:

$Area_{semicircle} = \frac{1}{2} \pi r^2$

Using $\pi = 3.14$ and $r = 4$ yd:

$Area_{semicircle} = \frac{1}{2} \times 3.14 \times 4^2 = \frac{1}{2} \times 3.14 \times 16 = 3.14 \times 8 = 25.12 \, yd^2$

Finally, the area of the shaded region is the difference between the area of the rectangle and the area of the semicircle:

$Area_{shaded} = Area_{rectangle} - Area_{semicircle} = 64 - 25.12 = 38.88 \, yd^2$

3. Final Answer

38.88 yd^2