Find the value of the variable in the tetrahedron below. The height of the tetrahedron is 6 units and the volu

Question

Find the value of the variable in the tetrahedron below. The height of the tetrahedron is 6 units and the volume iscubic units. Recall that a tetrahedron is made up of four equilateral triangles. Show all work.
http://i40.photobucket.com/albums/e215/xxs3xp1stolxx/19.jpg

Answer 1

volume of a pyramid is Bh/3, so
6B/3 = 32√3
B = 16√3

base is equilateral triangle, edge x, area (x/2)(x/2)√3, so
x²/4 √3 = 16√3
x²/4 = 16
x² = 64
x = 8