The base of a triangular pyramid is a triangle with corners at (3 ,5 ), (4 ,2 ), and (2 ,6 ). If the pyramid has a height of 7 , what is the pyramid's volume?

1 Answer
Jun 29, 2017

The volume is =2.33u^3

Explanation:

The area of the base triangle is calculated with the determinant

Therefore, the area of the base is

A=1/2|(x_1,y_1,1),(x_2,y_2,1),(x_3,y_3,1)|

A=1/2|(3,5,1),(4,2,1),(2,6,1)|

=1/2(3*|(2,1),(6,1)|-5*|(4,1),(2,1)|+1*|(4,2),(2,6)|)

=1/2(3(2-6)-5(4-2)+1(24-4))

=1/2(-12-10+20)

=1/2|-2|=1

The volume of the pyramid is

=1/3*h*A=1/3*7*1=7/3=2.33u^3