Question

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

Answer 1

`color(maroon)("Volume of a pyramid "V_p = 1/3*A_b*h=18.67 " cubic.units"`

Explanation:

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

`(x_1,y_1)=(2,3) ,(x_2,y_2)=(5,1),(x_3,y_3)=(3,5) , h=7`

`color(crimson)("Area of Triangle "`

`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(2(1−5)+5(5−3)+3(3−1))| = 4`

`color(maroon)("Volume of a pyramid "V_p = 1/3*A_b*h=1/3 *8*7=56/3 = 18.67 " cubic.units"`