The base of a triangular pyramid is a triangle with corners at $(7 ,5 )$ , $(6 ,9 )$ , and $(3 ,4 )$ . If the pyramid has a height of $15$ , what is the pyramid's volume?

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Answer 1 · 2016-09-10T14:40:36

Area of a triangle given three vertices $(x_1, y_1)$ , $(x_2,y_2)$ , $(x_3,y_3)$ is:

$A = abs((x_1(y_2-y_3) + x_2(y_3-y_1) +x_3(y_1-y_2))/2$

$(x_1,y_1) =(7,5)$
$(x_2,y_2)=(6,9)$
$(x_3,y_3) =(3,4)$

$A=abs((7(9-4)+6(4-5)+3(5-9))/2$

$A=abs((7*-5+6*-1+3*-4)/2$

$A=abs((-35-6-12)/2$

$A=abs(-53/2) =26.5$

Volume of a trianglar pyramid = $V= 1/3Ah$ where A is the area of the triangular base and h is the height of the pyramid.

$V=1/3*26.5*15 = 132.5$

The base of a triangular pyramid is a triangle with corners at (7 ,5 )(7 ,5 ), (6 ,9 )(6 ,9 ), and (3 ,4 )(3 ,4 ). If the pyramid has a height of 15 15 , what is the pyramid's volume?