The base of a triangular pyramid is a triangle with corners at #(3 ,8 )#, #(4 ,1 )#, and #(9 ,8 )#. If the pyramid has a height of #4 #, 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)=(3,8),(x_2,y_2)=(4,1),(x_3,y_3)=(9,8)#
#A=1/2|3(1-8)+4(8-8)+9(8-1)|#
#color(white)(A)=1/2|-21+0+72|=51/2#
#V=1/3xx51/2xx4=34" units"^3#
