The base of a triangular pyramid is a triangle with corners at $(3, 8)$ $(3 ,8 )$ , $(1, 6)$ $(1 ,6 )$ , and $(2, 8)$ $(2 ,8 )$ . If the pyramid has a height of $4$ $4$ , what is the pyramid's volume?

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The base of a triangular pyramid is a triangle with corners at $(3, 8)$ $(3 ,8 )$ , $(1, 6)$ $(1 ,6 )$ , and $(2, 8)$ $(2 ,8 )$ . If the pyramid has a height of $4$ $4$ , what is the pyramid's volume?

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Answer 1 · 2018-06-09T19:22:07

$\frac{8}{3}$ $\frac{8}{3}$ units^2

Explanation:

The area of the base (triangle) can be worked out from the vertices, as

Area = ${2 \cdot 2} {2} = 2$ ${2 * 2}{2} = 2$

Therefore by using the formula

$V = {A \cdot h} {3}$ $V = {A * h}{3}$ we get the volume as $\frac{2 \cdot 4}{3} = \frac{8}{3}$ $\frac{2*4}{3} = \frac{8}{3}$

Answer 2 · 2018-06-10T02:52:35

$Volume of a pyramid V_{p} = \frac{1}{3} \cdot A_{b} \cdot h = \frac{1}{3} \cdot 1 \cdot 4 = \frac{4}{3}$ $color(blue)("Volume of a pyramid "V_p = 1/3*A_b*h=1/3 *1*4 = 4/3$

Explanation:

$Area of triangle knowing three vertices on the coordinate plane is given by$ $"Area of triangle knowing three vertices on the coordinate plane is given by "$

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

$(x_{1}, y_{1}) = (3, 8), (x_{2}, y_{2}) = (1, 6), (x_{3}, y_{3}) = (2, 8), h = 4$ $(x_1,y_1)=(3,8) ,(x_2,y_2)=(1,6),(x_3,y_3)=(2,8) , h=4$

$A_{b} = ∣ ∣ ∣ \frac{1}{2} (3 (6 - 8) + 1 (8 - 8) + 2 (8 - 6)) ∣ ∣ ∣ = 1$ $A_b = |1/2(3(6−8)+1(8−8)+2(8−6))| = 1$

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

$Volume of a pyramid V_{p} = \frac{1}{3} \cdot A_{b} \cdot h = \frac{1}{3} \cdot 1 \cdot 4 = \frac{4}{3}$ $color(blue)("Volume of a pyramid "V_p = 1/3*A_b*h=1/3 *1*4 = 4/3$

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The base of a triangular pyramid is a triangle with corners at $(3, 8)$ $(3 ,8 )$ , $(1, 6)$ $(1 ,6 )$ , and $(2, 8)$ $(2 ,8 )$ . If the pyramid has a height of $4$ $4$ , what is the pyramid's volume?

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Explanation:

Explanation:

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The base of a triangular pyramid is a triangle with corners at (3,8)(3 ,8 ), (1,6)(1 ,6 ), and (2,8)(2 ,8 ). If the pyramid has a height of 44 , what is the pyramid's volume?

2 Answers

Explanation:

Explanation:

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The base of a triangular pyramid is a triangle with corners at $(3, 8)$ $(3 ,8 )$ , $(1, 6)$ $(1 ,6 )$ , and $(2, 8)$ $(2 ,8 )$ . If the pyramid has a height of $4$ $4$ , what is the pyramid's volume?