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

1 Answer
Jun 24, 2017

The volume of the pyramid is =4/3u^3

Explanation:

The area of the base triangle is

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

A=1/2|(3,4,1),(2,7,1),(3,6,1)|

=1/2(3*|(7,1),(6,1)|-4*|(2,1),(3,1)|+1*|(2,7),(3,6)|)

=1/2(3(7-6)-4(2-3)+1(12-21))

=1/2(3+4-9)

=1/2|-2|=1

The height is h=4

The volume of the pyramid is

V=1/3*A*h

=1/3*1*4=4/3