Make a cartogram! The area of each rectangle is fixed. Find the right shape (aspect ratio) for each rectangle and fit them into the bounding box. The layout at the bottom left shows you the correct adjacencies (that is, which rectangles should be neighboring and how).
Use your mouse to change the shape of a rectangle.
Move two rectangles close - they will snap together.
If two rectangles form a bigger rectangle in the layout, then matching their common edge automatically groups them into one rectangle. You can then use this group as if it was a single rectangle. Watch out for the red alignment indicators (cross and T-shape), if your rectangles are not properly aligned, then they cannot be merged.
Build the cartogram by iteratively grouping adjacent rectangles which form a larger rectangle.
Build the cartogram as quickly as possible! (Note: no high score is recorded if you play with high L-shape support.)
See how it's done: hit the "magic" button and watch how the cartogram is build.