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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?

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Get Cross

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?

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Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

Right angled triangle of sides 3,4 and 5 units

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