Question

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

Answer 1

Volume of pyramid `color(blue)(V = (1/3) A_b * h = (1/3) 4.76 * 4 = 6.35` cu. units

Explanation:

Triangular pyramid

Given : base corners and height.

To find the volume using formula `V = (1/3) A_b * h`

`A_b = sqrt(s (s-a) s- b) (s - c))` where s is the semi perimeter of the the triangular base and a,b,c are the three sides of the base. h is the height of the pyramid.

`a = sqrt((6-2)^2 + (8-6)^2)= 4.47`

`b = sqrt((2-2)^2 + (8-5)^2) = 3`

`c = sqrt ((6-5)^2 + (8-5)^2) = 3.16`

`s = (4.47 + 3 + 3.16) / 2 = 5.32`

`A_b = sqrt(5.32 * (5.32 - 4.47) (5.32-3) (5.32-3.16)) = 4.76`

Volume of pyramid `color(blue)(V = (1/3) A_b * h = (1/3) 4.76 * 4 = 6.35` cu. units