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?

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Answer 1 · 2016-12-30T08:40:31

$30 unit^3$

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

$Base Area = 6 unit^2$

$Volume = 1/3*6*15$
$Volume = 30 unit^3$

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