The base of a triangular pyramid is a triangle with corners at #(2 ,5 )#, #(6 ,4 )#, and #(7 ,8 )#. If the pyramid has a height of #4 #, what is the pyramid's volume?
1 Answer
Jan 31, 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 triangle can be found using"#
#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)=(2,5),(x_2,y_2)=(6,4),(x_3,y_3)=(7,8)#
#A=1/2|2(4-8)+6(8-5)+7(5-4)|#
#color(white)(A)=1/2|-8+18+7|=17/2#
#rArrV=1/3xx17/2xx4=34/3" cubic units"#
