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Ladder and Cube

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?

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Doesn't Add Up

In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

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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.

At Right Angles

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2
How do you get from one vertex of a square to the next one?
How far across? How far up?
And to the next vertex? And to the next? And back to the start?