The base of a triangular pyramid is a triangle with corners at (5,1), (2,7), and (3,4). If the pyramid has a height of 4, what is the pyramid's volume?

1 Answer

2 unit^3

Explanation:

Volume of pyramid #=1/3 x base area x height

Let x1=5,x2=2,x3=3,y1=1,y2=7andy3=4

Base area =12[[(x1y2)+(x2y3)+(x3y1)][(y1x2)+(y2x3)+(y3x1)]]

=12[[(57)+(24)+(31)][(12)+(73)+(45)]]
=12[(35+8+3)(2+21+20)]
=12(4643)
=32unit2

The volume =13324=2unit3