The base of a triangular pyramid is a triangle with corners at $(1, 3)$ $(1 ,3 )$ , $(2, 2)$ $(2 ,2 )$ , and $(8, 5)$ $(8 ,5 )$ . If the pyramid has a height of $7$ $7$ , what is the pyramid's volume?

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Answer 1 · 2017-09-12T11:12:02

Volume of pyramid is $10.5$ $10.5$ cu.unit.

$x_{1} = 1, y_{1} = 3, x_{2} = 2, y_{2} = 2, x_{3} = 8, y_{3} = 5$ $x_1=1 ,y_1=3 ,x_2=2 ,y_2=2,x_3=8 ,y_3=5$

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

$A_{t} = \frac{1}{2} (1 (2 - 5) + 2 (5 - 3) + 8 (3 - 2))$ $A_t= 1/2(1(2−5)+2(5−3)+8(3−2))$ or

$A_{t} = \frac{1}{2} (- 3 + 4 + 8) = \frac{9}{2} = 4.5$ $A_t= 1/2(-3+4+8)= 9/2 =4.5$ sq.unit

Volume of pyramid is $V_{p} = \frac{1}{3} \cdot A_{b} \cdot h;$ $V_p=1/3*A_b*h ;$ where base area

is $A_{b} = A_{t} = 4.5, h = 7$ $A_b = A_t= 4.5 , h=7$ ( hight).

$:.V_p=1/3*4.5*7 = 10.5$ cu.unit.

Volume of pyramid is $10.5$ cu.unit. [Ans]

The base of a triangular pyramid is a triangle with corners at (1 ,3 )(1,3)(1 ,3 ), (2 ,2 )(2,2)(2 ,2 ), and (8 ,5 )(8,5)(8 ,5 ). If the pyramid has a height of 7 77 , what is the pyramid's volume?