The goal area is 20 yards wide and 6 yards deep. It is the smaller of the two areas in front of the goal. The other area is called the penalty area.
It the area around the goal where a foul is punished with a penalty. It is not an ark however, but a box around the goal, 18 long.
You are probably referring to the penalty mark.
the Crease
If you've ever seen college lacrosse there's a circle around the goal that's the crease
interception
edge of an area
Basic science
The area around the equator where trade winds meet are called
The penalty area is 44 yards (40.23 m) wide and 18 yards (16.5 m) deep. It is the larger of the two areas in front of the goal. The other area is called the goal area.
umbilical area
The area around a magnet where its magnetic force is felt is called the magnetic field.