Question

The base of a triangular pyramid is a triangle with corners at `(6 ,2 )`, `(8 ,7 )`, and `(3 ,4 )`. If the pyramid has a height of `8`, what is the pyramid's volume?

Answer 1

Volume of the pyramid is #`25 1/3` cubic.unit.

Explanation:

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

`(x_1,y_1)=(6,2) ,(x_2,y_2)=(8,7),(x_3,y_3)=(3,4) , h=8`

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

`A_b = |1/2(6(7−4)+8(4−2)+3(2−7))|` or

`A_b = |1/2(18+16-15)| = | 19/2| =19/2`sq.unit

Volume of the pyramid is `1/3*A_b*h = 1/3 *19/2*8 = 76/3`

`25 1/3`cubic.unit [Ans]