The base of a triangular pyramid is a triangle with corners at (2 ,5 ), (6 ,3 ), and (7 ,8 ). If the pyramid has a height of 15 , what is the pyramid's volume?

1 Answer
Nov 1, 2016

55

Explanation:

A(2;5)" " B(6;3)" " C(7;8)

AB=2sqrt(5)

The line passing through A and B is

y-5=(3-5)/(6-2)*(x-2)

that in implicit form gets

x+2y-12=0

The distance of C from AB is

h=|1*7+2*8-12|/sqrt(5)=(23-12)/sqrt(5)=11/sqrt(5)

The base area is

AB*h/2=2*sqrt(5)*11/(2*sqrt(5))=11

The volume of pyramid is

("base area " xx " heigth")/3=11*15/3=55