Problem

Source: Bangladesh Mathematical Olympiad 2015, Secondary, P5

Tags: national olympiad, tetrahedron, Volume, area, algebra, geometry, 3D geometry



A tetrahedron is a polyhedron composed of four triangular faces. Faces ABC and BCD of a tetrahedron ABCD meet at an angle of π/6. The area of triangle ABC is 120. The area of triangle BCD is 80, and BC=10. What is the volume of the tetrahedron? We call the volume of a tetrahedron as one-third the area of it's base times it's height.