2D shapes and their properties

Work out the radius of a roll of adhesive tape.

A spiropath is a sequence of connected line segments end to end taking different directions. The same spiropath is iterated. When does it cycle and when does it go on indefinitely?

Weekly Problem 53 - 2007
The diagram shows a regular pentagon and regular hexagon which overlap. What is the value of x?

Weekly Problem 23 - 2008
A triangle has been drawn inside this circle. Can you find the length of the chord it forms?

M is any point on the line AB. Squares of side length AM and MB are constructed and their circumcircles intersect at P (and M). Prove that the lines AD and BE produced pass through P.

Can you work out the area of the inner square and give an explanation of how you did it?

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

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.

With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.

By inscribing a circle in a square and then a square in a circle find an approximation to pi. By using a hexagon, can you improve on the approximation?