The base of a triangular pyramid is a triangle with corners at $(1, 2)$ $(1 ,2 )$ , $(3, 1)$ $(3 ,1 )$ , and $(4, 3)$ $(4 ,3 )$ . 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 $(1, 2)$ $(1 ,2 )$ , $(3, 1)$ $(3 ,1 )$ , and $(4, 3)$ $(4 ,3 )$ . If the pyramid has a height of $6$ $6$ , what is the pyramid's volume?

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Answer 1 · 2018-06-10T02:42:43

$Volume of a pyramid V_{p} = \frac{1}{3} \cdot A_{b} \cdot h = \frac{1}{3} \cdot (\frac{5}{2}) \cdot 6 = 5 cubic.units$ $color(blue)("Volume of a pyramid "V_p = 1/3*A_b*h=1/3 *(5/2)*6 = 5 " cubic.units"$

Explanation:

$Volume of a pyramid V_{p} = \frac{1}{3} \cdot A_{b} \cdot h$ $color(crimson)("Volume of a pyramid " V_p = 1/3* A_b * h$

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

$Area of Triangle knowing three vertices on the coordinate plan is given by$ $color(crimson)("Area of Triangle knowing three vertices on the coordinate plan is given by "$

$A_{b} = ∣ ∣ ∣ \frac{1}{2} (x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})) ∣ ∣ ∣$ $color(crimson)(A_b = |1/2(x_1(y_2−y_3)+x_2(y_3−y_1)+x_3(y_1−y_2))|$

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

$Volume of a pyramid V_{p} = \frac{1}{3} \cdot A_{b} \cdot h = \frac{1}{3} \cdot (\frac{5}{2}) \cdot 6 = 5 cubic.units$ $color(blue)("Volume of a pyramid "V_p = 1/3*A_b*h=1/3 *(5/2)*6 = 5 " cubic.units"$

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The base of a triangular pyramid is a triangle with corners at $(1, 2)$ $(1 ,2 )$ , $(3, 1)$ $(3 ,1 )$ , and $(4, 3)$ $(4 ,3 )$ . 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 (1,2)(1 ,2 ), (3,1)(3 ,1 ), and (4,3)(4 ,3 ). 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 $(1, 2)$ $(1 ,2 )$ , $(3, 1)$ $(3 ,1 )$ , and $(4, 3)$ $(4 ,3 )$ . If the pyramid has a height of $6$ $6$ , what is the pyramid's volume?