The base of a triangular pyramid is a triangle with corners at (7,5), (6,9), and (3,4). If the pyramid has a height of 15, what is the pyramid's volume?

1 Answer
Sep 10, 2016

Area of a triangle given three vertices (x1,y1) , (x2,y2), (x3,y3) is:

A=x1(y2y3)+x2(y3y1)+x3(y1y2)2

(x1,y1)=(7,5)
(x2,y2)=(6,9)
(x3,y3)=(3,4)

A=7(94)+6(45)+3(59)2

A=75+61+342

A=356122

A=532=26.5

Volume of a trianglar pyramid = V=13Ah where A is the area of the triangular base and h is the height of the pyramid.

V=1326.515=132.5