Originally Posted by
VonNemo19 Let $\displaystyle A_1=\pi{(15.7)}^2-\frac{\frac{\pi}{4}}{2\pi}\pi{(15.7)}^2=\pi{15.7}^ 2-\frac{\pi(15.7)^2}{8}=\frac{7\pi(15.7)^2}{8}$ be the area the goat can graze in a circle around the pen from when the rope (fully extended) is paralel to BC until it is parallel to AB.
Let $\displaystyle A_2=\frac{1}{4}\pi{(15.7-\sqrt{162})^2}$ be the remaining quarter circile <<< (?) the goat can graze after its tether makes contact with point A.
Then the area the goat can graze is given by:
$\displaystyle A_1+A_2=...$