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Bangladesh Mathematical Olympiad 2015, Secondary, P5

Source: Bangladesh Mathematical Olympiad 2015, Secondary, P5

April 1, 2015
national olympiadtetrahedronVolumeareaalgebrageometry3D geometry

Problem Statement

A tetrahedron is a polyhedron composed of four triangular faces. Faces ABCABC and BCDBCD of a tetrahedron ABCDABCD meet at an angle of π/6\pi/6. The area of triangle △ABC\triangle ABC is 120120. The area of triangle △BCD\triangle BCD is 8080, and BC=10BC = 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.
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