Answer
$12r-(2+\frac{\pi}{2})r^2$
Work Step by Step
Step 1. Using the figure given in the exercise, the perimeter can be expressed as $\pi r+2r+2h=12$ which gives $h=6-r-\frac{\pi}{2}r$
Step 2. The area of the window is given by $A=\frac{\pi}{2}r^2+2rh=\frac{\pi}{2}r^2+2r(6-r-\frac{\pi}{2}r)=\frac{\pi}{2}r^2+12r-2r^2-\pi r^2=12r-(2+\frac{\pi}{2})r^2$
