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?

1 Answer
sankarankalyanam
Jun 10, 2018

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

Explanation:

#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"#

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