Question

The base of a triangular pyramid is a triangle with corners at `(5 ,8 )`, `(6 ,7 )`, and `(2 ,3 )`. If the pyramid has a height of `15`, what is the pyramid's volume?

Answer 1

The volume of the pyramid is `20` cubic units.

Explanation:

The volume of a pyramid is given by `1/3*`base area `*`height.

`(x_1,y_1)-=(5,8) ,(x_2,y_2)-=(6,7),(x_3,y_3)-=(2,3) , h=15`

Area of Triangle is

`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(5(7−3)+6(3−8)+2(8−7))|` or

`A_b = |1/2(20-30+2)| = | -8/2| =4` sq.unit.

So, the volume of the pyramid is `1/3*A_b*h = 1/3 *4*15 = 20` cubic units. [Ans]