The base of a triangular pyramid is a triangle with corners at #(4 ,5 )#, #(6 ,7 )#, and #(7 ,3 )#. If the pyramid has a height of #15 #, what is the pyramid's volume?

1 Answer
Jim G.
Feb 10, 2018

#"volume "=25#

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

#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)=(4,5),(x_2,y_2)=(6,7),(x_3,y_3)=(7,3)#

#A=1/2|4(7-3)+6(3-5)+7(5-7)|#

#color(white)(A)=1/2|16-12-14|=1/2xx10=5#

#rArrV=1/3xx5xx15=25#

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