Question

The base of a triangular pyramid is a triangle with corners at `(1 ,2 )`, `(3 ,1 )`, and `(4 ,3 )`. If the pyramid has a height of `6`, what is the pyramid's volume?

Answer 1

`color(blue)("Volume of a pyramid "V_p = 1/3*A_b*h=1/3 *(5/2)*6 = 5 " cubic.units"`

Explanation:

`color(crimson)("Volume of a pyramid " V_p = 1/3* A_b * h`

`(x_1,y_1)=(1,2) ,(x_2,y_2)=(3,1),(x_3,y_3)=(4,3) , h=7`

`color(crimson)("Area of Triangle knowing three vertices on the coordinate plan is given by "`

`color(crimson)(A_b = |1/2(x_1(y_2−y_3)+x_2(y_3−y_1)+x_3(y_1−y_2))|`

`A_b = |1/2(1(1−3)+3(3−2)+4(2−1))| = 5/2`

`color(blue)("Volume of a pyramid "V_p = 1/3*A_b*h=1/3 *(5/2)*6 = 5 " cubic.units"`