You'd probably have to check algorithmically. Starting from the top-left most piece, have they (reasonably fuzzily) covered the 6x10 grid proceeding down and right? If so, yay! You can also check for things like too much overlap, but checking if there is a piece covering each of the centers of the relative grid should be sufficient.

My first solution: http://i.imgur.com/rV2Ueow.png

edit: It also was not clear up front that I could click to rotate/flip the pieces, until I did it by accident.