Stage: 5 Challenge Level: 
In a tetrahedron two of the faces are identical equilateral triangles - side length $1$ unit. The other two faces are right angled isosceles triangles. Without using a calculator find the exact volume of the tetrahedron. (The result will involve a surd).
Pythagorean triples. Similarity. Tetrahedra. Right angled triangles. Pythagoras' theorem. Volume and capacity. Long problems. Mathematical reasoning & proof. Equilateral triangles. Circles.
Published November 2001.
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