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?

1 Answer
Dec 30, 2016

30 unit^330unit3

Explanation:

Volume of pyramic
= 1/3*basearea*height=13baseareaheight

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))]=12[((25)+(68)+(75))((56)+(57)+(82))]
= 1/2[(10+48+35) - (30+35+16)]=12[(10+48+35)(30+35+16)]
= 1/2(93-81)=12(9381)
= 1/2*12=1212 =6

Base Area = 6 unit^2BaseArea=6unit2

Volume = 1/3*6*15Volume=13615
Volume = 30 unit^3Volume=30unit3