The base of a triangular pyramid is a triangle with corners at #(6 ,8 )#, #(2 ,4 )#, and #(4 ,3 )#. If the pyramid has a height of #2 #, what is the pyramid's volume?

2 Answers
Mar 28, 2016

the volume of a triangular prism is V = (1/3)Bh where B is the area of the Base (in your case it would be the triangle) and h is the height of the pyramid.

This is a nice video demonstrating how to find the area of a triangular pyramid video

Now your next question might be :How do you find area of a triangle with 3 sides

Mar 28, 2016

to find the area of the BASE (triangle), you will need the length of each side and then use Heron's formula.
This is a nice web link showing you how to use Heron's formula and even has a built in calculator for this:

Heron's formula

Firstly, to determine the length of each side for the triangular base, you will need to use Pythagorus and determine the distance between each pair of points for the vertices of the triangle.

For example, the distance between points A(6, 8) and B(2, 4) is given by AB =#sqrt((6-2)^2+(8-4)^2# or #4sqrt2#
and the distance between points A(6, 8) and C(4, 3) is
AC =#sqrt((6-4)^2+(8-3)^2# or #sqrt29#

and now you need to find the distance between points B(2, 4) and C(4, 3).
Once you have the 3 distances, you can plug them into Heron's formula to get the area of the base.
With the area of the Base, you can then multiply by the height of the pyramid and divide by 3 to get the volume.