The base of a triangular pyramid is a triangle with corners at $(1 ,4 )$ , $(6 ,2 )$ , and $(8 ,5 )$ . If the pyramid has a height of $7$ , what is the pyramid's volume?

Question

1486 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-10T05:44:19

$color (orange)("Volume of Pyramid " V_p = (1/3) A_t * h = 70/3 " cub. units"$

$A (1,4), B(6,2), C(8,5), h = 7$

![https://www.onlinemathlearning.com/http://area-triangle.html](https://useruploads.socratic.org/AEeXSYYtQsKEBSfTbOQ1_Area%20of%20Triangles.png)

$A_t = (1/2) ^ |x_1 (y_2 - y_3) + x_2 (y-3 - y_1) + x_3 (y_1 - y_2)|$

$A_t = (1/2) |1 (6-8) + 6 (5-4) + 8 (4-2)| = 10$

$color (orange)("Volume of Pyramid " V_p = (1/3) A_t * h = (1/3) * 10 * 7 = 70/3 " cub. units"$

The base of a triangular pyramid is a triangle with corners at (1 ,4 )(1 ,4 ), (6 ,2 )(6 ,2 ), and (8 ,5 )(8 ,5 ). If the pyramid has a height of 7 7 , what is the pyramid's volume?