Question

The base of a triangular pyramid is a triangle with corners at `(3 ,8 )`, `(4 ,9 )`, and `(2 ,6 )`. If the pyramid has a height of `7`, what is the pyramid's volume?

Answer 1

`"volume "=7/6`

Explanation:

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

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

`"the area of the triangle can be 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)=(3,8),(x_2,y_2)=(4,9),(x_3,y_3)=(2,6)`

`rArrA=1/2|3(9-6)+4(6-8)+2(8-9)|`

`color(white)(rArrA)=1/2|9-8-2|=1/2xx1=1/2`

`rArrV=1/3xx1/2xx7=7/6`