The base of a triangular pyramid is a triangle with corners at #(3 ,2 )#, #(5 ,6 )#, and #(2 ,8 )#. If the pyramid has a height of #12 #, what is the pyramid's volume?

1 Answer
Jim G.
Mar 6, 2018

#"volume "=32#

Explanation:

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

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

#"the area (A) of the base 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)=(3,2),(x_2,y_2)=(5,6),(x_3,y_3)=(2,8)#

#A=1/2|(3(6-8)+5(8-2)+2(2-6)|#

#color(white)(A)=1/2|-6+30-8|=8#

#rArrV=1/3xx8xx12=32#

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