Length/distance

Can you prove that the sum of the distances of any point inside a square from its sides is always equal (half the perimeter)? Can you prove it to be true for a rectangle or a hexagon?

The Earth is further from the Sun than Venus, but how much further? Twice as far? Ten times?

Weekly Problem 48 - 2008
An ant is crawling in a straight line when he bumps into a one centimetre cube of sugar.If he climbs over it before before continuing on his intended route, how much does the detour add to the length of his journey?

Use simple trigonometry to calculate the distance along the flight path from London to Sydney.

Can you choose your units so that a cube has the same numerical value for it volume, surface area and total edge length?

Mark writes four points on a line at different lengths. What is the distance between the two points furthest apart?

Tom and Tim are travelling towards Glasgow, but leave at different times. If Tim overtakes Tom, how fast is he travelling?

Four vehicles travelled on a road. What can you deduce from the times that they met?

Use your hand span to measure the distance around a tree trunk. If you ask a friend to try the same thing, how do the answers compare?

You will need a long strip of paper for this task. Cut it into different lengths. How could you find out how long each piece is?