The base of a triangular pyramid is a triangle with corners at $(6 ,2 )$ , $(2 ,7 )$ , and $(3 ,4 )$ . If the pyramid has a height of $8$ , what is the pyramid's volume?

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Answer 1 · 2017-09-13T11:19:43

Volume of pyramid is $9 1/3$ cu.unit.

Volume of pyramid $V_p= 1/3 * B * h$ ,where $B$ is base area and

h is hght of pyramid . If $(x1, x2), (x2, y2) and (x3, y3)$ are the

coordinates of vertices of triangle then area of triangle is

$A_t= 1/2(x1(y2−y3)+x2(y3−y1)+x3(y1−y2))$ or

$A_t= 1/2(6(7−4)+2(4−2)+3(2−7))$ or

$A_t= 1/2(18+4-15) = 3.5$

Volume of pyramid $V_p= 1/3 * B * h = 1/3 *3.5 *8 =28/3$ cu.unit

Volume of pyramid is $9 1/3$ cu.unit [Ans]

The base of a triangular pyramid is a triangle with corners at (6 ,2 )(6 ,2 ), (2 ,7 )(2 ,7 ), and (3 ,4 )(3 ,4 ). If the pyramid has a height of 8 8 , what is the pyramid's volume?