a softball diamond is a square with one corner at home plate, so:

area = length * width

the problem statement lacks clarity and in order to solve this we will assume the path-path of width 'x' lies with equal amounts on either side of the border of the diamond itself, therefore the total area of the diamond including the base-path is extended by x/2 along both the 1st and 3rd base lines

the diamond then effectively becomes a square with sides of '45' and '45 + x/2' (the base-path to 1st base extends both the 2nd and home baselines on the first-base side of the diamond, while the base-path from 3rd extends both the 1st and 3rd baselines on the third-base side of the diamond)

total area of the softball diamond including a base path of width 'x':

area = (45+x/2)(45+x/2) = (1/4)(x+90)^2

the total area of the software diamond, including the base-paths under our assumptions, is (1/4)(x+90)^2