How to cut up polygons with a grid in ArcMap?

[JoshSwain]

I have the basic license and have a set of buildings represented as polygons over a map, I would like to cut these polygons up with an overlaying grid so that I can measure what percent of area of each grid space is covered by the building. I tried clipping, intersecting, and unionizing the build by the grid to no avail.

[David]

Why didn't an intersect work? that should split any overlapping boundaries and leave you with your original building polygons. You could create 2 new fields: One to store the area of the new split building section and another to divided it by the sum for that building.