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?

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Answer 1 · 2017-09-13T11:19:43

Volume of pyramid is $9 \frac{1}{3}$ $9 1/3$ cu.unit.

Volume of pyramid $V_{p} = \frac{1}{3} \cdot B \cdot h$ $V_p= 1/3 * B * h$ ,where $B$ $B$ is base area and

h is hght of pyramid . If $(x 1, x 2), (x 2, y 2) and (x 3, y 3)$ $(x1, x2), (x2, y2) and (x3, y3)$ are the

coordinates of vertices of triangle then area of triangle is

$A_{t} = \frac{1}{2} (x 1 (y 2 - y 3) + x 2 (y 3 - y 1) + x 3 (y 1 - y 2))$ $A_t= 1/2(x1(y2−y3)+x2(y3−y1)+x3(y1−y2))$ or

$A_{t} = \frac{1}{2} (6 (7 - 4) + 2 (4 - 2) + 3 (2 - 7))$ $A_t= 1/2(6(7−4)+2(4−2)+3(2−7))$ or

$A_{t} = \frac{1}{2} (18 + 4 - 15) = 3.5$ $A_t= 1/2(18+4-15) = 3.5$

Volume of pyramid $V_{p} = \frac{1}{3} \cdot B \cdot h = \frac{1}{3} \cdot 3.5 \cdot 8 = \frac{28}{3}$ $V_p= 1/3 * B * h = 1/3 *3.5 *8 =28/3$ cu.unit

Volume of pyramid is $9 \frac{1}{3}$ $9 1/3$ 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 88 , what is the pyramid's volume?