The base of a triangular pyramid is a triangle with corners at $(2, 6)$ $(2 ,6 )$ , $(4, 3)$ $(4 ,3 )$ , and $(3, 8)$ $(3 ,8 )$ . If the pyramid has a height of $6$ $6$ , what is the pyramid's volume?

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The base of a triangular pyramid is a triangle with corners at $(2, 6)$ $(2 ,6 )$ , $(4, 3)$ $(4 ,3 )$ , and $(3, 8)$ $(3 ,8 )$ . If the pyramid has a height of $6$ $6$ , what is the pyramid's volume?

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Answer 1 · 2018-01-27T10:05:23

Volume pf pyramid $V_{p} = 14$ $color(indico)(V_p =14)$ cubic units

Explanation:

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Volume of Triangular pyramid $V_{p} = (\frac{1}{3}) B H$ $V_p = (1/3) B H$ where B is the base area of the triangle and H is the height of the pyramid.

$the area (A) of the triangle can be found using the formula given the coordinates of the three vertices$ $"the area (A) of the triangle can be found using the formula given the coordinates of the three vertices"$

$B = \frac{1}{2} [x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})]$ $B=1/2[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]$

$B = [2 (3 - 8) + (4 (8 - 6) + 3 (6 - 3)] = (- 10 + 8 + 9) = 7$ $color(red)(B =) [2(3-8) + (4(8-6) + 3(6-3)] = (-10 + 8 + 9) = color(red)(7)$

Volume pf pyramid $V_{p} = (\frac{1}{3}) B H = (\frac{1}{3}) \cdot 7 \cdot 6 = 14$ $color(red)(V_p = (1/3) B H = (1/3) * 7 * 6 = color(red)(14)$ cubic units

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The base of a triangular pyramid is a triangle with corners at $(2, 6)$ $(2 ,6 )$ , $(4, 3)$ $(4 ,3 )$ , and $(3, 8)$ $(3 ,8 )$ . If the pyramid has a height of $6$ $6$ , what is the pyramid's volume?

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The base of a triangular pyramid is a triangle with corners at (2,6)(2 ,6 ), (4,3)(4 ,3 ), and (3,8)(3 ,8 ). If the pyramid has a height of 66 , what is the pyramid's volume?

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The base of a triangular pyramid is a triangle with corners at $(2, 6)$ $(2 ,6 )$ , $(4, 3)$ $(4 ,3 )$ , and $(3, 8)$ $(3 ,8 )$ . If the pyramid has a height of $6$ $6$ , what is the pyramid's volume?