Pythagoras' theorem

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

Draw a square and an arc of a circle and construct the Golden rectangle. Find the value of the Golden Ratio.

Chris is enjoying a swim but needs to get back for lunch. How far along the bank should she land?

The net of a cube is to be cut from a sheet of card 100 cm square. What is the maximum volume cube that can be made from a single piece of card?

A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance up the wall which the ladder can reach?

A rectangular piece of paper is folded. Can you work out one of the lengths in the diagram?

Find out how many pieces of hardboard of differing sizes can fit through a rectangular window.

A ribbon runs around a box so that it makes a complete loop with two parallel pieces of ribbon on the top. How long will the ribbon be?

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

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