The base of a triangular pyramid is a triangle with corners at (7 ,6 ), (4 ,3 ), and (1 ,5 ). If the pyramid has a height of 6 , what is the pyramid's volume?

1 Answer
Jim G.
Mar 22, 2018

15" units"^3

Explanation:

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

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

"the area (A) of the triangular base is found 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)=(7,6),(x_2,y_2)=(4,3),(x_3,y_3)=(1,5)

A=1/2|7(3-5)+4(5-6)+1(6-3)|

color(white)(A)=1/2|-14-4+3|=1/2|-15|=15/2

rArrV=1/3xx15/2xx6=15" units"^3

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