The base of a triangular pyramid is a triangle with corners at $(4, 5)$ $(4 ,5 )$ , $(6, 1)$ $(6 ,1 )$ , and $(7, 3)$ $(7 ,3 )$ . If the pyramid has a height of $15$ $15$ , what is the pyramid's volume?

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The base of a triangular pyramid is a triangle with corners at $(4, 5)$ $(4 ,5 )$ , $(6, 1)$ $(6 ,1 )$ , and $(7, 3)$ $(7 ,3 )$ . If the pyramid has a height of $15$ $15$ , what is the pyramid's volume?

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Answer 1 · 2018-01-10T10:32:58

Volume of a pyramid is $20$ $20$ cubic.unit.

Explanation:

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

$(x_{1}, y_{1}) = (4, 5), (x_{2}, y_{2}) = (6, 1), (x_{3}, y_{3}) = (7, 3), h = 15$ $(x_1,y_1)=(4,5) ,(x_2,y_2)=(6,1),(x_3,y_3)=(7,3) , h=15$

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

$A_{b} = ∣ ∣ ∣ \frac{1}{2} (4 (1 - 3) + 6 (3 - 5) + 7 (5 - 1)) ∣ ∣ ∣$ $A_b = |1/2(4(1−3)+6(3−5)+7(5−1))|$ or

$A_{b} = ∣ ∣ ∣ \frac{1}{2} (- 8 - 12 + 28) ∣ ∣ ∣ = \frac{1}{2} \cdot 8 = 4$ $A_b = |1/2(-8-12+28)| =1/2 *8 =4$ sq.unit.

Volume of a pyramid is $\frac{1}{3} \cdot A_{b} \cdot h = \frac{1}{3} \cdot 4 \cdot 15 = 20$ $1/3*A_b*h = 1/3 *4*15 = 20$ cubic.unit [Ans]

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The base of a triangular pyramid is a triangle with corners at $(4, 5)$ $(4 ,5 )$ , $(6, 1)$ $(6 ,1 )$ , and $(7, 3)$ $(7 ,3 )$ . If the pyramid has a height of $15$ $15$ , 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 (4,5)(4 ,5 ), (6,1)(6 ,1 ), and (7,3)(7 ,3 ). If the pyramid has a height of 1515 , 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 $(4, 5)$ $(4 ,5 )$ , $(6, 1)$ $(6 ,1 )$ , and $(7, 3)$ $(7 ,3 )$ . If the pyramid has a height of $15$ $15$ , what is the pyramid's volume?