A 4" by 6" by 8" rectangular solid is cut by slicing through the midpoint of three adjacent edges. What is the number of inches in the sum of the lengths of the edges of the tetrahedron that is cut?

waffles
Apr 30, 2017

#1**+3 **

Maybe this will help:

sum of tetrahedron edges = red line + orange line + yellow line + green line + blue line + purple line

red line = \(\sqrt{3^2+2^2}=\sqrt{13}\)

orange line = \(\sqrt{3^2+4^2}=\sqrt{25}=5\)

yellow line = \(\sqrt{2^2+4^2}=\sqrt{20}=2\sqrt5\)

sum of tetrahedron edges = \(\sqrt{13}+5+2\sqrt5+3+2+4=14+\sqrt{13}+2\sqrt{5} \approx 22.078\)

hectictar
Apr 30, 2017