Covering rectangles in 2D

Hi,

I have a little problem and I hope somebody can put some light on it.
I also hope this is the correct group to ask as I did not find a
geometry group.

Suppose there is a big rectangle, 'A', and suppose that I put several
smaller rectangles over 'A'. The small rectangles can be overlapped,
but they are all inside 'A'. The question is, is it possible to know
whether 'A' is totally covered? In other words, it is possible to know
if all points inside 'A' are also inside of, at least, one small
rectangle?

Example:
'A' is the rectangle with coordinates (down-left corner and upper-
right corner) <0, 0> <100, 200>
There are two smaller rectangles: '1' is <0, 0> <50, 100>; '2' is
<50,100> <200, 200>.
In this case, 'A' is not totally covered because, for example, point
<70, 20> is not in any of the smaller rectangles.

Does this problem is solvable?

Thanks

.

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