Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

There are many different methods to solve this geometrical problem - how many can you find?

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

Stick some cubes together to make a cuboid. Find two of the angles by as many different methods as you can devise.

An environment that simulates a protractor carrying a right- angled triangle of unit hypotenuse.

A dot starts at the point (1,0) and turns anticlockwise. Can you estimate the height of the dot after it has turned through 45 degrees? Can you calculate its height?

Two ribbons are laid over each other so that they cross. Can you find the area of the overlap?

How much of the inside of this triangular prism can Clare paint using a cylindrical roller?