Constructions

The farmers want to redraw their field boundary but keep the area the same. Can you advise them?

Can you work out the side length of a square that just touches the hypotenuse of a right angled triangle?

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

Using a ruler, pencil and compasses only, it is possible to construct a square inside any triangle so that all four vertices touch the sides of the triangle.

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?

Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...

Design and construct a prototype intercooler which will satisfy agreed quality control constraints.

Investigate constructible images which contain rational areas.

Describe how to construct three circles which have areas in the ratio 1:2:3.