The base of a triangular pyramid is a triangle with corners at (2 ,5 ), (6 ,9 ), and (3 ,8 ). If the pyramid has a height of 15 , what is the pyramid's volume?

1 Answer
Shwetank Mauria
Mar 2, 2016

20.001

Explanation:

To find volume of a triangular pyramid of height 15 and base a triangle with corners at A(2,5), B(6,9), and C(3,8) we must find the area of the base triangle.

The sides of triangle can be found as follows.

AB=sqrt((6-2)^2+(9-5)^2)=sqrt32=5.6568

BC=sqrt((6-3)^2+(9-8)^2)=sqrt(9+1)=sqrt10=3.1623

CA=sqrt((3-2)^2+(8-5)^2)=sqrt(1+9)=sqrt10=3.1623

Using Heron's formula s=(5.6568+3.1623+3.1623)/2=5.9907

and area of triangle is sqrt(5.9907xx(5.9907-5.6568)xx(5.9907-3.1623)xx(5.9907-3.1623)
i.e. sqrt(5.9907xx0.3339xx2.8284xx2.8284)=sqrt16.0021=4.0002 (approx.)

As volume of pyramid 1/3xxheightxxarea of base, it is 1/3xx4.0002xx15=20.001

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