Pythagoras' theorem

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

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?

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

If two of the sides of a right-angled triangle are 5cm and 6cm long, how many possibilities are there for the length of the third side?

A ribbon is nailed down with a small amount of slack. What is the largest cube that can pass under the ribbon ?

Can you calculate the length of this diagonal line?

A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle

A white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing?

Equal circles can be arranged so that each circle touches four or six others. What percentage of the plane is covered by circles in each packing pattern? ...

Prove that the shaded area of the semicircle is equal to the area of the inner circle.