Question

The base of a triangular pyramid is a triangle with corners at `(2 ,5 )`, `(6 ,4 )`, and `(7 ,8 )`. If the pyramid has a height of `4`, what is the pyramid's volume?

Answer 1

Volume of the pyramid is `11 1/3` cubic.unit.

Explanation:

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

`(x_1,y_1)=(2,5) ,(x_2,y_2)=(6,4),(x_3,y_3)=(7,8) , h=4`

Area of Triangle is

`A_t = |1/2(x1(y2−y3)+x2(y3−y1)+x3(y1−y2))|`

`A_b = |1/2(2(4−8)+6(8−5)+7(5−4))|` or

`A_t = |1/2(-8+18+7)| = 1/2|17| =17/2`sq.unit.

Volume of pyramid is `1/3*A_b*h = 1/3 *17/2*4 = 34/3=11 1/3`

cubic.unit [Ans]