The base of a triangular pyramid is a triangle with corners at #(7 ,6 )#, #(4 ,3 )#, and #(1 ,5 )#. If the pyramid has a height of #6 #, what is the pyramid's volume?

1 Answer
Jim G.
Mar 22, 2018

#15" units"^3#

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 (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)=(7,6),(x_2,y_2)=(4,3),(x_3,y_3)=(1,5)#

#A=1/2|7(3-5)+4(5-6)+1(6-3)|#

#color(white)(A)=1/2|-14-4+3|=1/2|-15|=15/2#

#rArrV=1/3xx15/2xx6=15" units"^3#

Related questions
See all questions in Volume of Solids
Impact of this question
1594 views around the world
You can reuse this answer
Creative Commons License