The base of a triangular pyramid is a triangle with corners at $(5, 8)$ $(5 ,8 )$ , $(4, 1)$ $(4 ,1 )$ , and $(9, 3)$ $(9 ,3 )$ . 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 $(5, 8)$ $(5 ,8 )$ , $(4, 1)$ $(4 ,1 )$ , and $(9, 3)$ $(9 ,3 )$ . If the pyramid has a height of $4$ $4$ , what is the pyramid's volume?

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Answer 1 · 2018-02-11T12:29:34

Volume of the pyramid is $22$ $22$ cubic.unit .

Explanation:

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

$(x_{1}, y_{1}) = (5, 8), (x_{2}, y_{2}) = (4, 1), (x_{3}, y_{3}) = (9, 3), h = 4$ $(x_1,y_1)=(5,8) ,(x_2,y_2)=(4,1),(x_3,y_3)=(9,3) , h=4$

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

$A_{b} = ∣ ∣ ∣ \frac{1}{2} (5 (1 - 3) + 4 (3 - 8) + 9 (8 - 1)) ∣ ∣ ∣$ $A_b = |1/2(5(1−3)+4(3−8)+9(8−1))|$ or

$A_{b} = ∣ ∣ ∣ \frac{1}{2} (- 10 - 20 + 63) ∣ ∣ ∣ = ∣ ∣ ∣ \frac{33}{2} ∣ ∣ ∣ = 16.5$ $A_b = |1/2(-10-20+63)| = | 33/2| =16.5$ sq.unit.

Volume of a pyramid is $\frac{1}{3} \cdot A_{b} \cdot h = \frac{1}{3} \cdot \frac{33}{2} \cdot 4 = 22$ $1/3*A_b*h = 1/3*33/2*4 = 22$ cubic.unit
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The base of a triangular pyramid is a triangle with corners at $(5, 8)$ $(5 ,8 )$ , $(4, 1)$ $(4 ,1 )$ , and $(9, 3)$ $(9 ,3 )$ . If the pyramid has a height of $4$ $4$ , 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 (5,8)(5 ,8 ), (4,1)(4 ,1 ), and (9,3)(9 ,3 ). If the pyramid has a height of 44 , what is the pyramid's volume?

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Explanation:

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The base of a triangular pyramid is a triangle with corners at $(5, 8)$ $(5 ,8 )$ , $(4, 1)$ $(4 ,1 )$ , and $(9, 3)$ $(9 ,3 )$ . If the pyramid has a height of $4$ $4$ , what is the pyramid's volume?