Question

The base of a triangular pyramid is a triangle with corners at `(5 ,8 )`, `(4 ,3 )`, and `(9 ,4 )`. If the pyramid has a height of `4`, what is the pyramid's volume?

Answer 1

Volume of pyramid is `16` cubic unit.

Explanation:

`(x_1,y_1) = (5,8) ; (x_2,y_2) = (4,3) ; (x_3,y_3) = (9,4)`

Area of triangle with given vertices is `A_t=1/2(x_1(y_2-y_3) +x_2(y_3-y_1)+x_3(y_1-y_2)` or

`A_t=1/2(5(3-4) +4(4-8)+9(8-3)) = 1/2 (-5-16+45)=1/2*24=12` sq.unit

Given height of pyramid is `h=4`

Volume of a pyramid is `V=1/3*A_t*h= 1/3*12*4=16` cubic unit [Ans]