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2015 AMC 10AProblem 21P21-25~7 minPrint
Solid GeometryTriangles: Area & PythagoreanAdd construction lines/points (drop altitudes, extend segments, connect centers)Set up the equation/formula and compute; no special trick needed

Tetrahedron ABCDABCD has AB=5AB=5 , AC=3AC=3 , BC=4BC=4 , BD=4BD=4 , AD=3AD=3 , and CD=1252CD=\tfrac{12}5\sqrt2 . What is the volume of the tetrahedron?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.