The base of a triangular pyramid is a triangle with corners at (6 ,8 ), (2 ,7 ), and (7 ,3 ). If the pyramid has a height of 2 , what is the pyramid's volume?

1 Answer
Jim G.
Jun 21, 2018

7" units"^3

Explanation:

"the volume (V) of a pyramid is calculated using"

•color(white)(x)V=1/3xx"area of base"xx"height"

"the area (A) of the triangular base is calculated using"

•color(white)(x)A=1/2|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|

"let "(x_1,y_1)=(6,8),(x_2,y_2)=(2,7),(x_3,y_3)=(7,3)

A=1/2|6(7-3)+2(3-8)+7(8-7)|

color(white)(A)=1/2|24-10+7|=21/2

V=1/3xx21/2xx2=7" units"^3

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