Area - squares and rectangles

Have a good look at these images. Can you describe what is happening? There are plenty more images like this on NRICH's Exploring Squares CD.

What do these two triangles have in common? How are they related?

An investigation that gives you the opportunity to make and justify predictions.

How many tiles do we need to tile these patios?

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

How many ways can you find of tiling the square patio, using square tiles of different sizes?

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?

How many centimetres of rope will I need to make another mat just like the one I have here?