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?

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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?

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Answer 1 · 2016-12-30T08:40:31

$30 u n i t^{3}$ $30 unit^3$

Explanation:

Volume of pyramic
$= \frac{1}{3} \cdot b a s e a r e a \cdot h e i g h t$ $= 1/3*basearea*height$

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))]

$= \frac{1}{2} [((2 \cdot 5) + (6 \cdot 8) + (7 \cdot 5)) - ((5 \cdot 6) + (5 \cdot 7) + (8 \cdot 2))]$ $= 1/2[((2*5)+(6*8)+(7*5))-((5*6)+(5*7)+(8*2))]$
$= \frac{1}{2} [(10 + 48 + 35) - (30 + 35 + 16)]$ $= 1/2[(10+48+35) - (30+35+16)]$
$= \frac{1}{2} (93 - 81)$ $= 1/2(93-81)$
$= \frac{1}{2} \cdot 12$ $= 1/2*12$ =6

$B a s e A r e a = 6 u n i t^{2}$ $Base Area = 6 unit^2$

$V o l u m e = \frac{1}{3} \cdot 6 \cdot 15$ $Volume = 1/3*6*15$
$V o l u m e = 30 u n i t^{3}$ $Volume = 30 unit^3$

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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?

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Explanation:

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The base of a triangular pyramid is a triangle with corners at (2 ,5 )(2,5)(2 ,5 ), (6 ,5 )(6,5)(6 ,5 ), and (7 ,8 )(7,8)(7 ,8 ). If the pyramid has a height of 15 1515 , what is the pyramid's volume?

1 Answer

Explanation:

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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?