The base of a triangular pyramid is a triangle with corners at (7 ,6 ), (4 ,1 ), and (3 ,2 ). If the pyramid has a height of 7 , what is the pyramid's volume?

1 Answer
Mar 5, 2016

28/3 " cubic units"~=9.333 " cubic units"

Explanation:

Area of base, a triangle

S_(base)=(1/2)|[[x_1,y_1,1],[x_2,y_2,1],[x_3,y_3,1]]|
S_(base)=(1/2)|[[7,6,1],[4,1,1],[3,2,1]]| =(1/2)| [7+18+8-(3+14+24)] |=(1/2)|[33-41]|=(1/2) 8=4

The volume of a pyramid is
V=(S_(base)*height)/3
So

V=(4*7)/3=28/3 " cubic units"~=9.333 " cubic units"