Question

The base of a triangular pyramid is a triangle with corners at `(2 ,5 )`, `(1 ,6 )`, and `(2 ,8 )`. If the pyramid has a height of `4`, what is the pyramid's volume?

Answer 1

Volume of a pyramid is `2` cubic unit.

Explanation:

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

`(x_1,y_1)=(2,5) ,(x_2,y_2)=(1,6),(x_3,y_3)=(2,8) , h=4`

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

`A_b = |1/2(2(6−8)+1(8−5)+2(5−6))|` or

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

Volume of a pyramid is `1/3*A_b*h = 1/cancel3 *cancel3/2*4 = 2` cubic.unit [Ans]