The base of a triangular pyramid is a triangle with corners at $(3 ,2 )$ , $(5 ,6 )$ , and $(2 ,8 )$ . If the pyramid has a height of $12$ , what is the pyramid's volume?

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The base of a triangular pyramid is a triangle with corners at $(3 ,2 )$ , $(5 ,6 )$ , and $(2 ,8 )$ . If the pyramid has a height of $12$ , what is the pyramid's volume?

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Answer 1 · 2018-03-06T21:00:49

$"volume "=32$

Explanation:

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

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

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

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

$"let "(x_1,y_1)=(3,2),(x_2,y_2)=(5,6),(x_3,y_3)=(2,8)$

$A=1/2|(3(6-8)+5(8-2)+2(2-6)|$

$color(white)(A)=1/2|-6+30-8|=8$

$rArrV=1/3xx8xx12=32$

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The base of a triangular pyramid is a triangle with corners at $(3 ,2 )$ , $(5 ,6 )$ , and $(2 ,8 )$ . If the pyramid has a height of $12$ , 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 ,2 )(3 ,2 ), (5 ,6 )(5 ,6 ), and (2 ,8 )(2 ,8 ). If the pyramid has a height of 12 12 , 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 $(3 ,2 )$ , $(5 ,6 )$ , and $(2 ,8 )$ . If the pyramid has a height of $12$ , what is the pyramid's volume?