The base of a triangular pyramid is a triangle with corners at #(7 ,2 )#, #(4 ,3 )#, and #(9 ,5 )#. If the pyramid has a height of #6 #, what is the pyramid's volume?
1 Answer
Jul 30, 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 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)=(7,2),(x_2,y_2)=(4,3),(x_3,y_3)=(9,5)#
#A=1/2|7(3-5)+4(5-2)+9(2-3)|#
#color(white)(A)=1/2|-14+12-9|=11/2#
#V=1/3xx11/2xx6=11" units"^3#
