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?
1 Answer
Feb 9, 2018
Explanation:
#"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#
