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

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Answer 1 · 2018-06-10T02:42:43

$color(blue)("Volume of a pyramid "V_p = 1/3*A_b*h=1/3 *(5/2)*6 = 5 " cubic.units"$

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

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

![https://www.onlinemathlearning.com/http://area-triangle.html](https://useruploads.socratic.org/TCkef5lBQbWlcvUfPtgy_Area%20of%20Triangles.png)

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

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

$A_b = |1/2(1(1−3)+3(3−2)+4(2−1))| = 5/2$

$color(blue)("Volume of a pyramid "V_p = 1/3*A_b*h=1/3 *(5/2)*6 = 5 " cubic.units"$

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?