The base of a triangular pyramid is a triangle with corners at $(6, 7)$ $(6 ,7 )$ , $(2, 5)$ $(2 ,5 )$ , and $(3, 1)$ $(3 ,1 )$ . If the pyramid has a height of $4$ $4$ , what is the pyramid's volume?

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The base of a triangular pyramid is a triangle with corners at $(6, 7)$ $(6 ,7 )$ , $(2, 5)$ $(2 ,5 )$ , and $(3, 1)$ $(3 ,1 )$ . If the pyramid has a height of $4$ $4$ , what is the pyramid's volume?

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Answer 1 · 2018-01-13T11:36:25

Volume of a pyramid is $12$ $12$ cubic.unit.

Explanation:

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

$(x_{1}, y_{1}) = (6, 7), (x_{2}, y_{2}) = (2, 5), (x_{3}, y_{3}) = (3, 1), h = 4$ $(x_1,y_1)=(6,7) ,(x_2,y_2)=(2,5),(x_3,y_3)=(3,1) , h=4$

Area of Triangle is

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

$A_{b} = ∣ ∣ ∣ \frac{1}{2} (6 (5 - 1) + 2 (1 - 7) + 3 (7 - 5)) ∣ ∣ ∣$ $A_b = |1/2(6(5−1)+2(1−7)+3(7−5))|$ or

$A_{b} = ∣ ∣ ∣ \frac{1}{2} (24 - 12 + 6) ∣ ∣ ∣ = | 9 | = 9$ $A_b = |1/2(24-12+6)| = | 9| =9$ sq.unit.

Volume of a pyramid is $\frac{1}{3} \cdot A_{b} \cdot h = \frac{1}{3} \cdot 9 \cdot 4 = 12$ $1/3*A_b*h = 1/3 *9*4 = 12$ cubic.unit [Ans]

Answer 2 · 2018-01-13T11:47:59

$volume = 12$ $"volume "=12$

Explanation:

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

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

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

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

$let (x_{1}, y_{1}) = (6, 7), (x_{2}, y_{2}) = (2, 5), (x_{3}, y_{3}) = (3, 1)$ $"let "(x_1,y_1)=(6,7),(x_2,y_2)=(2,5),(x_3,y_3)=(3,1)$

$A = \frac{1}{2} | 6 (5 - 1) + 2 (1 - 7) + 3 (7 - 5) |$ $A=1/2|6(5-1)+2(1-7)+3(7-5)|$

$A = \frac{1}{2} | 24 - 12 + 6 | = \frac{1}{2} | 18 | = 9$ $color(white)(A)=1/2|24-12+6|=1/2|18|=9$

$\Rightarrow V = \frac{1}{3} \times 9 \times 4 = 12$ $rArrV=1/3xx9xx4=12$

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The base of a triangular pyramid is a triangle with corners at $(6, 7)$ $(6 ,7 )$ , $(2, 5)$ $(2 ,5 )$ , and $(3, 1)$ $(3 ,1 )$ . If the pyramid has a height of $4$ $4$ , 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 (6,7)(6 ,7 ), (2,5)(2 ,5 ), and (3,1)(3 ,1 ). If the pyramid has a height of 44 , what is the pyramid's volume?

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Explanation:

Explanation:

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The base of a triangular pyramid is a triangle with corners at $(6, 7)$ $(6 ,7 )$ , $(2, 5)$ $(2 ,5 )$ , and $(3, 1)$ $(3 ,1 )$ . If the pyramid has a height of $4$ $4$ , what is the pyramid's volume?