Question

The base of a triangular pyramid is a triangle with corners at `(5 ,8 )`, `(4 ,1 )`, and `(9 ,3 )`. If the pyramid has a height of `4`, what is the pyramid's volume?

Answer 1

Volume of the pyramid is `22` cubic.unit .

Explanation:

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

`(x_1,y_1)=(5,8) ,(x_2,y_2)=(4,1),(x_3,y_3)=(9,3) , h=4`

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

`A_b = |1/2(5(1−3)+4(3−8)+9(8−1))|` or

`A_b = |1/2(-10-20+63)| = | 33/2| =16.5`sq.unit.

Volume of a pyramid is `1/3*A_b*h = 1/3*33/2*4 = 22` cubic.unit
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