The base of a triangular pyramid is a triangle with corners at (2 5 ) (6 5 ) and (7 8 ). If the pyramid has a height of 15 what is the pyramid's volume?

##30 unit^3##
Volume of pyramic
##= 1/3*basearea*height##
Base area = 1/2x [ 2 6 7 2] [5 5 8 5]
the area calculation based on Cartesian coordinate (ab)(cd) and (ef)
=1/2*{a c e a][b d f b] = 1/2[((axd)+(cxf)+(exb))-((bxc)+(dxe)+(fxa))]
##= 1/2[((2*5)+(6*8)+(7*5))-((5*6)+(5*7)+(8*2))]##
##= 1/2[(10+48+35) – (30+35+16)]##
##= 1/2(93-81)##
## = 1/2*12## =6
##Base Area = 6 unit^2##
##Volume = 1/3*6*15##
##Volume = 30 unit^3##