The base of a triangular pyramid is a triangle with corners at (3 ,8 ), (4 ,2 ), and (9 ,8 ). If the pyramid has a height of 4 , what is the pyramid's volume?

1 Answer
jags
Jun 26, 2016

24

Explanation:

Given coordinates of Triangle ABC

A(3,8)
B(4,2)
C(9,8)

Given the coordinates of the three vertices of any triangle, the area of the triangle is given by:
area =
(Ax*( By − Cy ) + Bx*( Cy − Ay ) + Cx *( Ay − By ) )/2

where Ax and Ay are the x and y coordinates of the point A etc..

In our case, area = ( 3*(2-8) + 4*(8-8) + 9*(8-2))/2

Area = (3*(-6) + 4*0 + 9*6)/2

=> (-18+0+54)/2

=> 36/2 = 18

The volume of a triangular pyramid is V = 1/3AH where A = area of the triangle base, and H = height of the pyramid or the distance from the pyramid's base to the apex.

In our case, H=4. So volume = 1/3*18*4 = 24

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