Does it have to cover the whole screen without overlap? If not then just make shapes of random sizes and at random locations (that do not go off the screen). Keep a boolean array of length width*height. Every time you put a new shape down, set all of the elements in the array that correspond to the array to true. If all of the elements are true then you are done.

I just realized what I wrote might not be clear regarding the array. Here is an example:

the shapes have to start from the top left of the screen and go across in rows; once the row reaches the end of the screen, it will continue in a row beneath the previous one, and so forth. The shapes can't be cut off at the edges of the screen. 

Then just use shapes that you know the height and width of. If your width is 400, and you are using shapes that are 40 units wide then you know to move down a row after 10 shapes. If your height is 600 and your shapes are also 30 units tall then you know that after 20 rows you have covered the screen.

I know I need to declare what x and y are, but don't know what to declare them. hehe. Here is my code so far. The triangle's dimensions will change once I know what is going on in my code.