# The base of a triangular pyramid is a triangle with corners at #(2 ,1 )#, #(5 ,2 )#, and #(8 ,7 )#. If the pyramid has a height of #18 #, what is the pyramid's volume?

Volume of a triangular pyramid is:

Where

Dimensions of triangle:

Let the angles be at:

Using the distance formula:

Length

Finding

Area of triangle from diagram:

Area of pyramid:

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The volume of the triangular pyramid is 144 cubic units.

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