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'Changing Areas, Changing Perimeters' printed from

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Working on Area and Perimeter might give you some useful insights to help you to solve this problem. 
If you are having trouble making sense of the grid, have a look at this image. The robots have been arranged according to their width and height, in the same way that the cards need to be arranged according to their area and perimeter:
As you go from left to right, the width of the robots increases.
As you go from top to bottom, the height of the robots increases.
All the robots in the middle column have the same width.
All the robots on the middle row have the same height.