find the area of the plane section VAD.?

Question

V-ABC is a tetrahedron. D is the midpoint of the midpoint of BC. AB = AC = VB =VC. VC = 66 cm., VA = 38 cm., BC =51 cm.

Answer 1

Hmmmm.. tough one to do in text only with no pictures...

First, I will assume that V is the Vertex on the top of the tetrahedron and that the base is formed by the triangle ABC...

........66
A-------------B
..-..............-
....-..........-
66..-......- D (51 for full side, 25.5 for BD or DC)
........-..-
.........-
.........C

You know that AB is 66
You know that BC = 51 (so BD is 51/2 or 25.5)

What you are looking for is the area of VAD, so you need the lengths of the sides...

You are given VA = 38...

Since BAC is an Isoceles triangle (It does not look like it in my drawing but it is because AB = AC) then you can calculate the length of AD as the altitude...

BVC is also an Isoceles triangle since VB = VC.. so you can determine the length of DV as the altitude of this triangle...

Put the 3 sides together.. find the altitude and base.. and determine the area.