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The base of a triangular pyramid is a triangle with corners at #(2 ,6 )#, #(5 ,3 )#, and #(8 ,2 )#. If the pyramid has a height of #2 #, what is the pyramid's volume?

1 Answer

sankarankalyanam

Jun 10, 2018

#color(crimson)("Volume of pyramid " V_p = (1/3) * A_t * h = 28 " cub. units"#

Explanation:

#A (2,6), B (5,3), C (8,2), h = 2#

#"Area of base triangle " 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) (2 (3-2) + 5 (2-6) + 8 (6 - 3))| = 42#

#color(crimson)("Volume of pyramid " V_p = (1/3) * A_t * h = (1/3) * 42 * 2 = 28#

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