Visualising and representing

Can you make a tetrahedron whose faces all have the same perimeter?

A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?

The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

A circle is inscribed in an equilateral triangle. Smaller circles touch it and the sides of the triangle, the process continuing indefinitely. What is the sum of the areas of all the circles?

Imagine you are suspending a cube from one vertex and allowing it to hang freely. What shape does the surface of the water make around the cube?

Eight children each had a cube made from modelling clay. They cut them into four pieces which were all exactly the same shape and size. Whose pieces are the same? Can you decide who made each set?

Can you split each of the shapes below in half so that the two parts are exactly the same?

How would you find out how many football cards Catrina has collected?

Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape.