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?

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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?

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Answer 1 · 2018-03-06T21:00:49

$volume = 32$ $"volume "=32$

Explanation:

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

$∙ x V = \frac{1}{3} \times area of base \times height$ $•color(white)(x)V=1/3xx"area of base"xx"height"$

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

$∙ x A = \frac{1}{2} | x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2}) |$ $•color(white)(x)A=1/2|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|$

$let (x_{1}, y_{1}) = (3, 2), (x_{2}, y_{2}) = (5, 6), (x_{3}, y_{3}) = (2, 8)$ $"let "(x_1,y_1)=(3,2),(x_2,y_2)=(5,6),(x_3,y_3)=(2,8)$

$A = \frac{1}{2} ∣ (3 (6 - 8) + 5 (8 - 2) + 2 (2 - 6) ∣$ $A=1/2|(3(6-8)+5(8-2)+2(2-6)|$

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

$\Rightarrow V = \frac{1}{3} \times 8 \times 12 = 32$ $rArrV=1/3xx8xx12=32$

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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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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 1212 , 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 $(3, 2)$ $(3 ,2 )$ , $(5, 6)$ $(5 ,6 )$ , and $(2, 8)$ $(2 ,8 )$ . If the pyramid has a height of $12$ $12$ , what is the pyramid's volume?