The base of a triangular pyramid is a triangle with corners at $(4, 2)$ $(4 ,2 )$ , $(3, 6)$ $(3 ,6 )$ , and $(7, 5)$ $(7 ,5 )$ . 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 $(4, 2)$ $(4 ,2 )$ , $(3, 6)$ $(3 ,6 )$ , and $(7, 5)$ $(7 ,5 )$ . If the pyramid has a height of $6$ $6$ , what is the pyramid's volume?

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Answer 1 · 2018-06-09T02:21:07

$Volume of a pyramid V_{p} = \frac{1}{3} \cdot A_{b} \cdot h = 15 cubic.units$ $color(violet)("Volume of a pyramid " V_p = 1/3*A_b*h= 15" cubic.units"$

Explanation:

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

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

$Area of Triangle$ $color(indigo)("Area of Triangle "$

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

$A_{b} = ∣ ∣ ∣ \frac{1}{2} (4 (6 - 5) + 3 (5 - 2) + 7 (2 - 6)) ∣ ∣ ∣ = \frac{15}{2} sq units$ $A_b = |1/2(4(6−5)+3(5−2)+7(2−6))| = 15/2 " sq units"$

$Volume of a pyramid$ $color(violet)("Volume of a pyramid "$

$V_{p} = \frac{1}{3} \cdot A_{b} \cdot h = \frac{1}{3} \cdot \frac{15}{2} \cdot 6 = 15 cubic.unit$ $color(violet)(V_p = 1/3*A_b*h=1/3 *15/2*6= 15" cubic.unit"$

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The base of a triangular pyramid is a triangle with corners at $(4, 2)$ $(4 ,2 )$ , $(3, 6)$ $(3 ,6 )$ , and $(7, 5)$ $(7 ,5 )$ . 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 (4 ,2 )(4,2)(4 ,2 ), (3 ,6 )(3,6)(3 ,6 ), and (7 ,5 )(7,5)(7 ,5 ). If the pyramid has a height of 6 66 , 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 $(4, 2)$ $(4 ,2 )$ , $(3, 6)$ $(3 ,6 )$ , and $(7, 5)$ $(7 ,5 )$ . If the pyramid has a height of $6$ $6$ , what is the pyramid's volume?