Answer:
Area of the garden:
[tex]\begin{equation*} 398.93\text{ ft}^2 \end{equation*}[/tex]
Explanation:
Given the below parameters;
Length of the rectangle(l) = 23 ft
Width of the rectangle(w) = 14 ft
Value of pi = 3.14
Since the width of the rectangle is 14 ft, so the diameter(d) of the semicircle is also 14 ft.
The radius(r) of the semicircle will now be;
[tex]r=\frac{d}{2}=\frac{14}{2}=7\text{ ft}[/tex]
Let's now go ahead and determine the area of the semicircle using the below formula;
[tex]A_{sc}=\frac{\pi r^2}{2}=\frac{3.14*\left(7\right)^2}{2}=\frac{3.14*49}{2}=\frac{153.86}{2}=76.93\text{ ft}^2[/tex]
Let's also determine the area of the rectangle;
[tex]A_r=l*w=23*14=322\text{ ft}^2[/tex]
We can now determine the area of the garden by adding the area of the semicircle and that of the rectangle together;
[tex]\begin{gathered} Area\text{ of the garden = Area of semi circle + Area of rectangle } \\ =76.93+322 \\ =398.93\text{ ft}^2 \end{gathered}[/tex]
Therefore, the area of the garden is 398.93 ft^2
