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

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

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Answer 1 · 2018-06-20T13:16:52

$volume = 1 {units}^{3}$ $"volume "=1" units"^3$

Explanation:

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

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

$the area (A) of the triangular base is found using$ $"the area (A) of the triangular base is found using"$

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

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

$A = \frac{1}{2} | 3 (4 - 7) + 1 (7 - 5) + 4 (5 - 4) |$ $A=1/2|3(4-7)+1(7-5)+4(5-4)|$

$A = \frac{1}{2} | - 9 + 2 + 4 | = \frac{3}{2}$ $color(white)(A)=1/2|-9+2+4|=3/2$

$V = \frac{1}{3} \times \frac{3}{2} \times 2 = 1$ $V=1/3xx3/2xx2=1$

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The base of a triangular pyramid is a triangle with corners at $(3, 5)$ $(3 ,5 )$ , $(1, 4)$ $(1 ,4 )$ , and $(4, 7)$ $(4 ,7 )$ . If the pyramid has a height of $2$ $2$ , 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 (3,5)(3 ,5 ), (1,4)(1 ,4 ), and (4,7)(4 ,7 ). If the pyramid has a height of 22 , what is the pyramid's volume?

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