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

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

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Answer 1 · 2018-01-12T20:30:27

$"volume "=26/3$

Explanation:

$"the volume (V) of a pyramid is calculated using the formula"$

$•color(white)(x)V=1/3xx"area of base "xx" height"$

$"the area (A) of the triangle can be found using"$

$•color(white)(x)A=1/2|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|$

$"let "(x_1,y_1)=(3,7),(x_2,y_2)=(1,4),(x_3,y_3)=(4,2)$

$A=1/2|3(4-2)+1(2-7)+4(7-4)|$

$color(white)(A)=|6-5+12|=13$

$V=1/3xx13xx2=26/3$

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

1 Answer

Explanation:

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Impact of this question

Science

Math

Humanities

... and beyond

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

1 Answer

Explanation:

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Impact of this question

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