The arena management want to put a perimeter fence around the car park. how many metres of fencing would be needed,  not  including the arena and a 5 metre space for a gate?  

So we have the sides of the car park, which is a rectangle, meaning each two parallel sides are equal. We have two 100m sides and two 75m sides.
Since we need to leave out the arena (50m) and a 5m space for a gate, we just add all the sides and subtract what needs to be left out (55m).

So: 100m+100m+75m+75m-55m= 200m+150m-55m = 350m-55m = 295m