Answer
A) $N(w) = 75w+\frac{\pi}{8}w^2$
B) $3208.94\ in^2$
Work Step by Step
Part A
Let $N$ be the total area of the Norman window. The area of the window is the sum of the rectangular part and the semi circle. The area of the half circle is just half the area of a complete circle. Refer to the figure for the derivation of the function.
$$N(w) = 75w+\frac{\pi}{8}w^2.\tag{1}$$ Part B
Set $w= 36$ in equation $(1)$ to find the area.
$$\begin{aligned}
N(36) &= 75\cdot 36+\frac{\pi}{8}\cdot 36^2\\
&\approx 3208.94\ in^2.
\end{aligned}$$
