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Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of the pictures.

Tilted Squares

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

Four or Five

The diagram shows a large rectangle composed of 9 smaller rectangles. If each of these rectangles has integer sides, what could the area of the large rectangle be?

Changing Areas, Changing Perimeters

Age 11 to 14
Challenge Level

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.