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All players, except the penalty taker must be at least 10 yards away from the penalty spot when the penalty is taken. As the Penalty Area extends 18 yards from the goal line, and the Penalty Spot is 12 yards from the goal line, the distance from the Penalty Spot to the edge of the Penalty Area can be as little as 6 Yards. The Arc - not half circle - marks the area outside the Penalty Area, that is within 10 yards of the Penalty Spot, and therefore outside which players must be when the penalty is taken
It is called the penalty arc. It is to ensure that defenders are 10 yards from the penalty spot when a penalty kick is taken.
The formula for determining the area of a decagon is A = 2.5dt where t is the length of one edge and d is the distance between two parallel sides
square
The surface area goes as the edge ength squared, so if you double the edges you get four times the area