Answer
The maximum possible error when computing the area of the window is $~~16.7~cm^2$
Work Step by Step
Let $x$ be the length of one side of the square.
Then the radius of the semicircle is $\frac{x}{2}$
We can find an expression for the area:
$A = x^2+\frac{1}{2}~\pi~(\frac{x}{2})^2$
$A = x^2+\frac{\pi~x^2}{8}$
We can find $dA$:
$dA = (2x+\frac{2\pi ~x}{8})~dx$
$dA = (2x+\frac{\pi ~x}{4})~dx$
$dA = [2(60)+\frac{60\pi}{4}]~(0.1)$
$dA = 16.7~cm^2$
The maximum possible error when computing the area of the window is $~~16.7~cm^2$
