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?

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?

In a Spin

Stage: 4 Challenge Level:

What is the volume of the solid formed by rotating this right
angled triangle about the hypotenuse?

Can you generalise this for any right angled triangle with sides
of length $a$, $b$ and $c$, where $b$ is the hypotenuse?