+35 Problem 1.
A tetrahedron is considered trirectangular if one of the vertices forms 3 90-angles. What is the volume of a trirectangular tetrahedron ABCD if one its faces is a 8,10,12 triangle?
Problem 2.
Let ABCD be a trirectangular tetrahedron such that ADB, ADC, and BDC are all right angles. If △ADB, △BDC, and △ADC each have area 3,4 and 12 , respectively, what is the area of △ABC ?
Problem 3.
If Sophia randomly chose three distinct integers between 1 and 6 inclusive, what is the probability that these integers could be the side lengths of one of the faces of a trirectangular tetrahedron?
Problem 4.
Let ABCD be a tetrahedron (not necessarily trirectangular!) such that AB = CD = 4 , AC = BD = 5 , and AD = BC = 6. Evaluate the volume of ABCD.
*Hint: can you find a way to create a trirectangular tetrahedron to help solve this problem?
