# The base of a triangular pyramid is a triangle with corners at #(1 ,2 )#, #(5 ,5 )#, and #(2 ,7 )#. If the pyramid has a height of #9 #, what is the pyramid's volume?

##### 1 Answer

Jun 26, 2016

25.5

#### Explanation:

Given coordinates of Triangle ABC

A(1,2)

B(5,5)

C(2,7)

Given the coordinates of the three vertices of any triangle, the area of the triangle is given by:

area =

where Ax and Ay are the x and y coordinates of the point A etc..

In our case, area =

Area =

=>

=>

The volume of a triangular pyramid is V = 1/3AH where A = area of the triangle base, and H = height of the pyramid or the distance from the pyramid's base to the apex.

In our case, H=9. A=8.5 So volume =