Question

When finding the perimiter of a figure on a grid, why do you not count the spaces inside the grid?

Answer 1

Because the inside is the area, and the outside or exactly on the line is the perimeter 

Answer 2

Counting the 'spaces' inside the grid refers to finding the area of the shape, as that's what surface area is: the amount of space inside the shape, so the number of a certain size of spaces inside a grid. The perimeter is completely different. It is the distance around the side of the shape, i.e. the sum of the length of each of the shape's sides.