Question

The base of a triangular pyramid is a triangle with corners at `(7 ,2 )`, `(4 ,3 )`, and `(9 ,5 )`. If the pyramid has a height of `6`, what is the pyramid's volume?

Answer 1

`"volume "=11" units"^3`

Explanation:

`"the volume (V) of a pyramid is calculated using"`

`•color(white)(x)V=1/3xx"area of base"xx"height"`

`"the area (A) of the triangular base is found using"`

`•color(white)(x)A=1/2|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|`

`"let "(x_1,y_1)=(7,2),(x_2,y_2)=(4,3),(x_3,y_3)=(9,5)`

`A=1/2|7(3-5)+4(5-2)+9(2-3)|`

`color(white)(A)=1/2|-14+12-9|=11/2`

`V=1/3xx11/2xx6=11" units"^3`