The base of a triangular pyramid is a triangle with corners at #(6 ,8 )#, #(2 ,7 )#, and #(7 ,3 )#. If the pyramid has a height of #2 #, what is the pyramid's volume?
1 Answer
Jun 21, 2018
Explanation:
#"the volume (V) of a pyramid is calculated using"#
#•color(white)(x)V=1/3xx"area of base"xx"height"#
#"the area (A) of the triangular base is calculated 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)=(6,8),(x_2,y_2)=(2,7),(x_3,y_3)=(7,3)#
#A=1/2|6(7-3)+2(3-8)+7(8-7)|#
#color(white)(A)=1/2|24-10+7|=21/2#
#V=1/3xx21/2xx2=7" units"^3#
