Question

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

Answer 1

`"volume "=1" 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)=(3,5),(x_2,y_2)=(1,4),(x_3,y_3)=(4,7)`

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

`color(white)(A)=1/2|-9+2+4|=3/2`

`V=1/3xx3/2xx2=1`