Question

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?

Answer 1

2 unit^3

Explanation:

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

Let `x_1=5, x_2=2,x_3=3, y_1=1,y_2=7 and y_3=4`

Base area `=1/2[[(x_1*y_2)+(x_2*y_3)+(x_3*y_1)]-[(y_1*x_2)+(y_2*x_3)+(y_3*x_1)]]`

`=1/2[[(5*7)+(2*4)+(3*1)]-[(1*2)+(7*3)+(4*5)]]`
`=1/2 [(35+8+3)-(2+21+20)]`
`=1/2 (46-43)`
`=3/2 unit^2`

The volume `=1/3*3/2*4 = 2 unit^3`