The base of a triangular pyramid is a triangle with corners at #(3 ,8 )#, #(4 ,2 )#, and #(2 ,6 )#. If the pyramid has a height of #7 #, what is the pyramid's volume?

1 Answer
Apr 9, 2016

volume #= 28/3#

Explanation:

The volume of a pyramid is given by the formula:
#color(white)("XXX")V=1/3 hb# where #h# is the height and #b# is the area of the base.

We are given the height (#h=7#)
so we need to find the base.

Method 1: Use the Pythagorean Theorem to find distance between points then apply Heron's Formula for the Area.
(left as an exercise).

Method 2: Evaluate the Area of the Triangular Base as the Sum and Difference of Trapezoids:
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From the relationship between the triangle and the trapezoid segments we see that the area of the base of our pyramid is
#color(white)("XXX")b=7+5-8 =4#

Therefore the Volume of the pyramid is
#color(white)("XXX")V=1/3 xx 7 xx 4 =28/3#