Question

The base of a triangular pyramid is a triangle with corners at `(4 ,5 )`, `(6 ,1 )`, and `(7 ,3 )`. If the pyramid has a height of `15`, what is the pyramid's volume?

Answer 1

Volume of a pyramid is `20` cubic.unit.

Explanation:

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

`(x_1,y_1)=(4,5) ,(x_2,y_2)=(6,1),(x_3,y_3)=(7,3) , h=15`

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

`A_b = |1/2(4(1−3)+6(3−5)+7(5−1))|` or

`A_b = |1/2(-8-12+28)| =1/2 *8 =4` sq.unit.

Volume of a pyramid is `1/3*A_b*h = 1/3 *4*15 = 20` cubic.unit [Ans]