Is a penalty kick given if a foul is committed in the penalty arc?

Answer 1

Foul refers to direct free kick offences. Any defender committing a foul against an attacker in the area results in a penalty kick.

But, an attacker committing a foul against a defender would result in a direct free kick.

Answer 2

If a foul is given within the penalty arc (the D-shaped bit at the top and center of the penalty area), it will not result in a penalty kick. The area enclosed by the arc is not part of the penalty area. The arc's only purpose is to ensure that players remain 10 yards away from the ball during penalty kicks.