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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?

Doesn't Add Up

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

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.

Which Is Cheaper?

Age 14 to 16 Challenge Level:
A table might help:
 
Hours
parked
Cost
Car park A
Cost
Car Park B
1    
2    
3    
4    
5    
6    

Once you've constructed a table, how else might you represent the information?