Question

The base of a triangular pyramid is a triangle with corners at `(2 ,2 )`, `(3 ,1 )`, and `(7 ,3 )`. If the pyramid has a height of `6`, what is the pyramid's volume?

Answer 1

Volume of a pyramid is `6` cubic.unit

Explanation:

Volume of a pyramid is `1/3*`base area `*`hight.

`(x_1,y_1)=(2,2) ,(x_2,y_2)=(3,1),(x_3,y_3)=(7,3) , h=6`

Area of Triangle is `A_b = |1/2(x1(y2−y3)+x2(y3−y1)+x3(y1−y2))|`

`A_b = |1/2(2(1−3)+3(3−2)+7(2−1))|` or

`A_b = |1/2(-4+3+7)| = | 6/2| =3` sq.unit

Volume of a pyramid is `1/3*A_b*h = 1/cancel3 *cancel3*6 = 6`

cubic.unit [Ans]