Question

The base of a triangular pyramid is a triangle with corners at `(5 ,1 )`, `(3 ,4 )`, and `(4 ,8 )`. If the pyramid has a height of `5`, what is the pyramid's volume?

Answer 1

Volume of the pyramid is `9.17` cubic.unit.

Explanation:

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

`(x_1,y_1)=(5,1) ,(x_2,y_2)=(3,4),(x_3,y_3)=(4,8) , h=5`

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

`A_b = |1/2(5(4−8)+3(8−1)+4(1−4))|` or

`A_b = |1/2(-20+21-12)| = | -11/2| =11/2=5.5`sq.unit

Volume of pyramid is `1/3*A_b*h = 1/3*5.5*5 ~~9.17` cubic unit [Ans]