finding the z score with a given area

Usually you use a table 'backwards' for this.

Find the area in the body of the table and then see what z score it corresponds with.

I am assuming a normal distribution.

We can not find z without the details?

You will need to know where the area is (under the normal curve of distribution); is it from the mean to the right?; is it evenly distributed on both sides of the mean? etc.