A random point A

A random point P is uniformly distributed in a square of side length 1 unit.
Find the probability of the following events:-

• the distance from P to a fixed side of the square does not exceed x, (x < 1)
• the distance from P to the nearest side does not exceed x, ( x < 1/2)
• the distance from P to the centre does not exceed x, { x < 1/ sqrt. (2)}
• the distance from P to a fixed vertex of the square does not exceed x, ( x < or = 1/ sqrt. 2)