Skip over navigation
Can you prove that the sum of the distances of any point inside a square from its sides is always equal?
Can you prove it to be true for a rectangle or a regular hexagon?
Does the hexagon need to be regular?
Can you show the same is the case for a regular pentagon?
Does the pentagon need to be regular?
Pentagonal
Age 14 to 16
Challenge Level 
Can you prove that the sum of the distances of any point inside a square from its sides is always equal?
Can you prove it to be true for a rectangle or a regular hexagon?
Does the hexagon need to be regular?
Can you show the same is the case for a regular pentagon?
Does the pentagon need to be regular?
You may also like
A Scale for the Solar System
The Earth is further from the Sun than Venus, but how much further? Twice as far? Ten times?
Swimmers
Swimmers in opposite directions cross at 20m and at 30m from each end of a swimming pool. How long is the pool ?