The base of a triangular pyramid is a triangle with corners at $(7, 6)$ $(7 ,6 )$ , $(4, 1)$ $(4 ,1 )$ , and $(3, 2)$ $(3 ,2 )$ . If the pyramid has a height of $7$ $7$ , what is the pyramid's volume?

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The base of a triangular pyramid is a triangle with corners at $(7, 6)$ $(7 ,6 )$ , $(4, 1)$ $(4 ,1 )$ , and $(3, 2)$ $(3 ,2 )$ . If the pyramid has a height of $7$ $7$ , what is the pyramid's volume?

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Answer 1 · 2016-03-05T01:14:45

$\frac{28}{3} cubic units ≅ 9.333 cubic units$ $28/3 " cubic units"~=9.333 " cubic units"$

Explanation:

Area of base, a triangle

$S_(base)=(1/2)|[[x_1,y_1,1],[x_2,y_2,1],[x_3,y_3,1]]|$
$S_(base)=(1/2)|[[7,6,1],[4,1,1],[3,2,1]]| =(1/2)| [7+18+8-(3+14+24)] |=(1/2)|[33-41]|=(1/2) 8=4$

The volume of a pyramid is
$V=(S_(base)*height)/3$
So

$V=(4*7)/3=28/3 " cubic units"~=9.333 " cubic units"$

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The base of a triangular pyramid is a triangle with corners at $(7, 6)$ $(7 ,6 )$ , $(4, 1)$ $(4 ,1 )$ , and $(3, 2)$ $(3 ,2 )$ . If the pyramid has a height of $7$ $7$ , what is the pyramid's volume?

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Explanation:

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Humanities

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The base of a triangular pyramid is a triangle with corners at (7 ,6 )(7,6)(7 ,6 ), (4 ,1 )(4,1)(4 ,1 ), and (3 ,2 )(3,2)(3 ,2 ). If the pyramid has a height of 7 77 , 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 $(7, 6)$ $(7 ,6 )$ , $(4, 1)$ $(4 ,1 )$ , and $(3, 2)$ $(3 ,2 )$ . If the pyramid has a height of $7$ $7$ , what is the pyramid's volume?