The base of a triangular pyramid is a triangle with corners at $(2 ,7 )$ , $(5 ,3 )$ , and $(8 ,2 )$ . If the pyramid has a height of $2$ , what is the pyramid's volume?

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Answer 1 · 2018-03-26T08:12:49

$5.67$ cubic units

First Of All, Find the Area of the Triangular Base.

So, The Area of the Base of The Pyramid :-

$1/2{x_1(y_2 -y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)}$

[If The Coordiantes for the vertices of the triangles are $(x_1,y_1),$

$(x_2,y_2) and (x_3,y_3)$ respectively.]

$= 1/2{2(3-2) + 5(2-7) + 8(7 - 3)}$ sq. units

$= 1/2{2 -25 +40}$ sq. units

$= 1/2(17)$ sq. units

$= 8.5$ sq. units.

So, The Volume of The Triangular Pyramid

$= 1/3(ah)$ [Where $a$ is the area of the base and $h$ is the height of the pyramid.]

$= 1/3 (8.5*2)$ cubic units

$= 17/3$ cubic units

$=5.67$ cubic units (approx.)

Hope this helps.

The base of a triangular pyramid is a triangle with corners at (2 ,7 )(2 ,7 ), (5 ,3 )(5 ,3 ), and (8 ,2 )(8 ,2 ). If the pyramid has a height of 2 2 , what is the pyramid's volume?