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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.

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Tilted Squares

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

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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?

Fence It

Age 11 to 14 Challenge Level:

Imagine you had $40$ one-metre sections of fencing.

What is the largest rectangular area of land you could fence off?

Now imagine you could build your fence up against a wall, so you only need to use the fence for three sides of the enclosure:


What is the largest area you can fence off now?

Now imagine you can attach the fence to the wall shown below, at the point marked X.
L shaped enclosure

What is the largest area you can fence off now?


Extension
Could you enclose even greater areas if you had $40$m of flexible wire fencing that could fence off curves as well as straight lines?