The base of a triangular pyramid is a triangle with corners at $(2, 6)$ $(2 ,6 )$ , $(5, 3)$ $(5 ,3 )$ , and $(8, 2)$ $(8 ,2 )$ . 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 $(2, 6)$ $(2 ,6 )$ , $(5, 3)$ $(5 ,3 )$ , and $(8, 2)$ $(8 ,2 )$ . If the pyramid has a height of $2$ $2$ , what is the pyramid's volume?

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Answer 1 · 2018-06-10T05:15:36

$Volume of pyramid V_{p} = (\frac{1}{3}) \cdot A_{t} \cdot h = 28 cub. units$ $color(crimson)("Volume of pyramid " V_p = (1/3) * A_t * h = 28 " cub. units"$

Explanation:

$A (2, 6), B (5, 3), C (8, 2), h = 2$ $A (2,6), B (5,3), C (8,2), h = 2$

$Area of base triangle A - T = ∣ ∣ ∣ (\frac{1}{2}) (x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})) ∣ ∣ ∣$ $"Area of base triangle " A-T = |(1/2)( x_1 (y_2-y_3) + x_2 (y_3 - y_1) + x_3 (y_1 - y_2))|$

$A_{t} = ∣ ∣ ∣ (\frac{1}{2}) (2 (3 - 2) + 5 (2 - 6) + 8 (6 - 3)) ∣ ∣ ∣ = 42$ $A_t = |(1/2) (2 (3-2) + 5 (2-6) + 8 (6 - 3))| = 42$

$Volume of pyramid V_{p} = (\frac{1}{3}) \cdot A_{t} \cdot h = (\frac{1}{3}) \cdot 42 \cdot 2 = 28$ $color(crimson)("Volume of pyramid " V_p = (1/3) * A_t * h = (1/3) * 42 * 2 = 28$

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The base of a triangular pyramid is a triangle with corners at $(2, 6)$ $(2 ,6 )$ , $(5, 3)$ $(5 ,3 )$ , and $(8, 2)$ $(8 ,2 )$ . 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 (2,6)(2 ,6 ), (5,3)(5 ,3 ), and (8,2)(8 ,2 ). 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 $(2, 6)$ $(2 ,6 )$ , $(5, 3)$ $(5 ,3 )$ , and $(8, 2)$ $(8 ,2 )$ . If the pyramid has a height of $2$ $2$ , what is the pyramid's volume?