12% = 0.12

Thus the radius of the polar ice

of the earth radius.

Arcsin(0.3464)= 0.35374 radians

Area of the segment viewed from a point where the latitude lines are parallel:

Approximately 3%.

NOTE: Your image indicates a side view of the earth at a point far from the earth and NORTH of latitude 69.73 degrees north. If you know the distance from the surface of the earth and the distance north or south of the equator a better approximation is possible. My calculation is for a flat latitude line. If you were at some point directly above the equator (some high altitude) the "shadow" of the polar ice would appear as crescent shaped.