The base of a triangular pyramid is a triangle with corners at (8 ,5 )(8,5), (6 ,2 )(6,2), and (5 ,9 )(5,9). If the pyramid has a height of 8 8, what is the pyramid's volume?
1 Answer
The volume is
Explanation:
The volume is the area of the base multiplied by the height:
Because we are given 3 points, the area is best computed using a determinant.
Here is a reference for the determinant that will help to compute the area given 3 points:
Substituting in the 3 points:
If find it easier to demonstrate the evaluation of a
Multiply each of the major diagonals and add them:
Multiply the minor diagonals and subtract them from the sum of the major diagonals:
Because the area cannot be negative, we choose the negative value for the
Using the