The base of a triangular pyramid is a triangle with corners at #(3 ,7 )#, #(1 ,4 )#, and #(4 ,2 )#. If the pyramid has a height of #2 #, what is the pyramid's volume?

1 Answer
Jim G.
Jan 12, 2018

#"volume "=26/3#

Explanation:

#"the volume (V) of a pyramid is calculated using the formula"#

#•color(white)(x)V=1/3xx"area of base "xx" height"#

#"the area (A) of the triangle can be found using"#

#•color(white)(x)A=1/2|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|#

#"let "(x_1,y_1)=(3,7),(x_2,y_2)=(1,4),(x_3,y_3)=(4,2)#

#A=1/2|3(4-2)+1(2-7)+4(7-4)|#

#color(white)(A)=|6-5+12|=13#

#V=1/3xx13xx2=26/3#

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