The base of a triangular pyramid is a triangle with corners at (1 ,2 ), (5 ,5 ), and (2 ,7 ). If the pyramid has a height of 9 , what is the pyramid's volume?
1 Answer
Jun 26, 2016
25.5
Explanation:
Given coordinates of Triangle ABC
A(1,2)
B(5,5)
C(2,7)
Given the coordinates of the three vertices of any triangle, the area of the triangle is given by:
area =
where Ax and Ay are the x and y coordinates of the point A etc..
In our case, area =
Area =
=>
=>
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=9. A=8.5 So volume =