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

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Answer 1 · 2018-06-09T19:22:07

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

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

Area = ${2 * 2}{2} = 2$

Therefore by using the formula

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

Answer 2 · 2018-06-10T02:52:35

$color(blue)("Volume of a pyramid "V_p = 1/3*A_b*h=1/3 *1*4 = 4/3$

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

$color(crimson)(A_b = |1/2(x_1(y_2−y_3)+x_2(y_3−y_1)+x_3(y_1−y_2))|$

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

$A_b = |1/2(3(6−8)+1(8−8)+2(8−6))| = 1$

$color(crimson)("Volume of a pyramid " V_p = 1/3* A_b * h$

$color(blue)("Volume of a pyramid "V_p = 1/3*A_b*h=1/3 *1*4 = 4/3$

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?