The base of a triangular pyramid is a triangle with corners at $(5 ,1 )$ , $(2 ,7 )$ , and $(3 ,6 )$ . If the pyramid has a height of $4$ , what is the pyramid's volume?

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Answer 1 · 2017-04-04T07:38:06

$2 unit^3$

Volume of pyramid = $1/3$ * base area * height

let say $x_1 = 5, x_2 = 2,x_3 = 3, y_1 = 1, y_2 = 7 and y_3 =6$

Base area $= 1/2 |(x_1*y_2 + x_2*y_3+x_3*y_1) - (y_1*x_2+y_2*x_3+y_3*x_1)|$

$= 1/2 |(5*7 + 2*6 + 3*1) - (1*2 + 7*3 + 6*5)|$

$= 1/2 |(35 + 12 + 3) - (2 + 21 + 30)|$

$= 1/2 |(50- 53)| = 1/2 |(-3)| = 3/2$

Volume of pyramid = $1/3 * 3/2 * 4 = 2 unit^3$

The base of a triangular pyramid is a triangle with corners at (5 ,1 )(5 ,1 ), (2 ,7 )(2 ,7 ), and (3 ,6 )(3 ,6 ). If the pyramid has a height of 4 4 , what is the pyramid's volume?