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 (x_1, y_1) , (x_2,y_2), (x_3,y_3) is:

A = abs((x_1(y_2-y_3) + x_2(y_3-y_1) +x_3(y_1-y_2))/2

(x_1,y_1) =(7,5)
(x_2,y_2)=(6,9)
(x_3,y_3) =(3,4)

A=abs((7(9-4)+6(4-5)+3(5-9))/2

A=abs((7*-5+6*-1+3*-4)/2

A=abs((-35-6-12)/2

A=abs(-53/2) =26.5

Volume of a trianglar pyramid = V= 1/3Ah where A is the area of the triangular base and h is the height of the pyramid.

V=1/3*26.5*15 = 132.5