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?

1 Answer
salamat
Dec 30, 2016

#30 unit^3#

Explanation:

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#

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