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