# The base of a triangular pyramid is a triangle with corners at #(3 ,8 )#, #(4 ,9 )#, and #(2 ,6 )#. If the pyramid has a height of #7 #, what is the pyramid's volume?

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Jim G.
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Feb 9, 2018

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#"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 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)=(3,8),(x_2,y_2)=(4,9),(x_3,y_3)=(2,6)#

#rArrA=1/2|3(9-6)+4(6-8)+2(8-9)|#

#color(white)(rArrA)=1/2|9-8-2|=1/2xx1=1/2#

#rArrV=1/3xx1/2xx7=7/6#

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