Question

7)
image of a rectangle with length 14 yd and a semicircular cutout (radius 5 yd) on the right side

Explanation:

Assuming we need to find the area of the rectangle with a semicircular cut - out (Problem 7):

Step 1: Find the area of the rectangle

The length of the rectangle \(l = 14\) yd. The diameter of the semicircle is equal to the width of the rectangle. The radius of the semicircle \(r = 5\) yd, so the diameter (width of rectangle) \(w=2r = 10\) yd.
The area of a rectangle is given by \(A_{rectangle}=l\times w\).
So, \(A_{rectangle}=14\times10 = 140\) square yards.

Step 2: Find the area of the semicircle

The formula for the area of a full circle is \(A_{circle}=\pi r^{2}\), so the area of a semicircle is \(A_{semicircle}=\frac{1}{2}\pi r^{2}\).
Substituting \(r = 5\) yd, we get \(A_{semicircle}=\frac{1}{2}\times\pi\times5^{2}=\frac{25\pi}{2}\approx\frac{25\times3.14}{2}=39.25\) square yards.

Step 3: Find the area of the figure

The area of the figure is the area of the rectangle minus the area of the semicircle.
\(A = A_{rectangle}-A_{semicircle}=140 - 39.25=100.75\) square yards. (If we use \(\pi=\frac{22}{7}\), then \(A_{semicircle}=\frac{1}{2}\times\frac{22}{7}\times5^{2}=\frac{1}{2}\times\frac{22}{7}\times25=\frac{275}{7}\approx39.29\), and \(A = 140-\frac{275}{7}=\frac{980 - 275}{7}=\frac{705}{7}\approx100.71\) square yards)

Answer:

If we assume the problem is to find the area, the answer is approximately \(100.75\) square yards (or \(\frac{705}{7}\approx100.71\) square yards if \(\pi = \frac{22}{7}\))