Next, find EG

The intersection o is EG vertical line and the vertical foot is H.

OC=2, so OH= root number 3, OG=6, so GH= root number 33, so EG=2 root number 33.

Therefore, the horizontal width AC=4, the vertical height AC =3, and the root number 1 1.

So S△AEG=6 root 1 1=S shadow.