The base of a triangular pyramid is a triangle with corners at $(1, 2)$ $(1 ,2 )$ , $(9, 5)$ $(9 ,5 )$ , and $(4, 7)$ $(4 ,7 )$ . If the pyramid has a height of $9$ $9$ , what is the pyramid's volume?

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The base of a triangular pyramid is a triangle with corners at $(1, 2)$ $(1 ,2 )$ , $(9, 5)$ $(9 ,5 )$ , and $(4, 7)$ $(4 ,7 )$ . If the pyramid has a height of $9$ $9$ , what is the pyramid's volume?

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Answer 1 · 2018-04-01T11:46:09

Volume of a pyramid is $46.5$ $46.5$ cubic.unit.

Explanation:

Volume of a pyramid is $\frac{1}{3} \cdot$ $1/3*$ base area $\cdot$ $*$ hight.

$(x_{1}, y_{1}) = (1, 2), (x_{2}, y_{2}) = (9, 5), (x_{3}, y_{3}) = (4, 7), h = 9$ $(x_1,y_1)=(1 ,2) ,(x_2,y_2)=(9,5),(x_3,y_3)=(4,7) , h=9$

Area of Triangle is $A_{b} = ∣ ∣ ∣ \frac{1}{2} (x 1 (y 2 - y 3) + x 2 (y 3 - y 1) + x 3 (y 1 - y 2)) ∣ ∣ ∣$ $A_b = |1/2(x1(y2−y3)+x2(y3−y1)+x3(y1−y2))|$

$A_{b} = ∣ ∣ ∣ \frac{1}{2} (1 (5 - 7) + 9 (7 - 2) + 4 (2 - 5)) ∣ ∣ ∣$ $A_b = |1/2(1(5−7)+9(7−2)+4(2−5))|$ or

$A_{b} = ∣ ∣ ∣ \frac{1}{2} (- 2 + 45 - 12) ∣ ∣ ∣ = ∣ ∣ ∣ \frac{31}{2} ∣ ∣ ∣ = \frac{31}{2}$ $A_b = |1/2(-2+45-12)| = | 31/2| =31/2$ sq.unit

Volume of a pyramid is $\frac{1}{3} \cdot A_{b} \cdot h = \frac{1}{3} \cdot \frac{31}{2} \cdot 9 = 46.5$ $1/3*A_b*h = 1/3 *31/2*9 = 46.5$

cubic.unit [Ans]

Answer 2 · 2018-04-01T11:46:14

$volume = \frac{93}{2}$ $"volume "=93/2$

Explanation:

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

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

$the area of the base (A) is calculated using$ $"the area of the base (A) is calculated using"$

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

$let (x_{1}, y_{1}) = (1, 2), (x_{2}, y_{2}) = (9, 5), (x_{3}, y_{3}) = (4, 7)$ $"let "(x_1,y_1)=(1,2),(x_2,y_2)=(9,5),(x_3,y_3)=(4,7)$

$A = \frac{1}{2} | 1 (5 - 7) + 9 (7 - 2) + 4 (2 - 5) |$ $A=1/2|1(5-7)+9(7-2)+4(2-5)|$

$A = \frac{1}{2} | - 2 + 45 - 12 | = \frac{31}{2}$ $color(white)(A)=1/2|-2+45-12|=31/2$

$\Rightarrow V = \frac{1}{3} \times \frac{31}{2} \times 9 = \frac{93}{2}$ $rArrV=1/3xx31/2xx9=93/2$

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The base of a triangular pyramid is a triangle with corners at $(1, 2)$ $(1 ,2 )$ , $(9, 5)$ $(9 ,5 )$ , and $(4, 7)$ $(4 ,7 )$ . If the pyramid has a height of $9$ $9$ , what is the pyramid's volume?

2 Answers

Explanation:

Explanation:

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Science

Math

Humanities

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The base of a triangular pyramid is a triangle with corners at (1 ,2 )(1,2)(1 ,2 ), (9 ,5 )(9,5)(9 ,5 ), and (4 ,7 )(4,7)(4 ,7 ). If the pyramid has a height of 9 99 , what is the pyramid's volume?

2 Answers

Explanation:

Explanation:

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The base of a triangular pyramid is a triangle with corners at $(1, 2)$ $(1 ,2 )$ , $(9, 5)$ $(9 ,5 )$ , and $(4, 7)$ $(4 ,7 )$ . If the pyramid has a height of $9$ $9$ , what is the pyramid's volume?