Problem 4

Part of 1990 French Mathematical Olympiad

Problems(1)

tetrahedron inscribed in cube, maximum area

Source: France 1990 P4

(a) What is the maximum area of a triangle with vertices in a given square (or on its boundary)? (b) What is the maximum volume of a tetrahedron with vertices in a given cube (or on its boundary)?

geometry3D geometrytetrahedron