The base of a triangular pyramid is a triangle with corners at $(3, 4)$ $(3 ,4 )$ , $(2, 7)$ $(2 ,7 )$ , and $(3, 6)$ $(3 ,6 )$ . If the pyramid has a height of $4$ $4$ , what is the pyramid's volume?

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Answer 1 · 2017-06-24T08:25:55

The volume of the pyramid is $= \frac{4}{3} u^{3}$ $=4/3u^3$

The area of the base triangle is

$A=1/2|(x_1,y_1,1),(x_2,y_2,1),(x_3,y_3,1)|$

$A=1/2|(3,4,1),(2,7,1),(3,6,1)|$

$=1/2(3*|(7,1),(6,1)|-4*|(2,1),(3,1)|+1*|(2,7),(3,6)|)$

$=1/2(3(7-6)-4(2-3)+1(12-21))$

$=1/2(3+4-9)$

$=1/2|-2|=1$

The height is $h=4$

The volume of the pyramid is

$V=1/3*A*h$

$=1/3*1*4=4/3$

The base of a triangular pyramid is a triangle with corners at (3 ,4 )(3,4)(3 ,4 ), (2 ,7 )(2,7)(2 ,7 ), and (3 ,6 )(3,6)(3 ,6 ). If the pyramid has a height of 4 44 , what is the pyramid's volume?