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 (a,b),(c,d) and (e,f) =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##