The base of a triangular pyramid is a triangle with corners at #(6 ,4 )#, #(2 ,1 )#, and #(3 ,2 )#. If the pyramid has a height of #4 #, what is the pyramid's volume?

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Answer 1 · 2018-06-09T02:11:56

#color(blue)(V_p = 1/3*A_b*h = 2/3 = 0.667 " cubic.units"#

#"Volume of a pyramid " V_p = 1/3* A_b * h#

#(x_1,y_1)=(6,4) ,(x_2,y_2)=(2,1),(x_3,y_3)=(3,2) , h=4#

Area of Triangle is

#A_b = |1/2(x_1(y_2−y_3)+x_2(y_3−y_1)+x_3(y_1−y_2))|#

#A_b = |1/2(6(1−2)+2(2−4)+3(4−1))| = 1/2#

Volume of a pyramid is

#color(blue)(V_p = 1/3*A_b*h=1/3 *1/2*4=2/3 = 0.667 " cubic.units"#