The base of a triangular pyramid is a triangle with corners at #(4 ,2 )#, #(3 ,6 )#, and #(7 ,5 )#. If the pyramid has a height of #6 #, what is the pyramid's volume?

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Answer 1 · 2018-06-09T02:21:07

#color(violet)("Volume of a pyramid " V_p = 1/3*A_b*h= 15" cubic.units"#

#color(purple)("Volume of a pyramid " V_p = 1/3* A_b * h#

#(x_1,y_1)=(4,2) ,(x_2,y_2)=(3,6),(x_3,y_3)=(7,5) , h=6#

#color(indigo)("Area of Triangle "#

#color(indigo)(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(4(6−5)+3(5−2)+7(2−6))| = 15/2 " sq units"#

#color(violet)("Volume of a pyramid " #

#color(violet)(V_p = 1/3*A_b*h=1/3 *15/2*6= 15" cubic.unit"#