#### You may also like

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

### From All Corners

Straight lines are drawn from each corner of a square to the mid points of the opposite sides. Express the area of the octagon that is formed at the centre as a fraction of the area of the square.

Kyle and his teacher disagree about his test score - who is right?

##### Age 14 to 16Challenge Level

Here is an 8 by 8 square that has been divided into four pieces:

Here is a rectangle made from the same four pieces:

You might like to try cutting out the shapes from a piece of paper.

It seems that the same pieces can make two shapes with different areas!
Can you explain where the extra area comes from?

Here are some questions you might like to consider:

Can other squares be split up and rearranged to make rectangles with a different area?

Are there other square/rectangle pairs where the areas differ by 1 square unit?

Is there a pattern in the sizes of squares that can be arranged in this way?