# The base of a triangular pyramid is a triangle with corners at #(3 ,5 )#, #(1 ,4 )#, and #(4 ,7 )#. If the pyramid has a height of #2 #, what is the pyramid's volume?

##### 1 Answer

Jun 20, 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)=(3,5),(x_2,y_2)=(1,4),(x_3,y_3)=(4,7)#

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

#color(white)(A)=1/2|-9+2+4|=3/2#

#V=1/3xx3/2xx2=1#