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?

Question

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?

1 Answer

Impact of this question

1167 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-04T07:38:06

$2 u n i t^{3}$ $2 unit^3$

Explanation:

Volume of pyramid = $\frac{1}{3}$ $1/3$ * base area * height

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

Base area $= \frac{1}{2} | (x_{1} \cdot y_{2} + x_{2} \cdot y_{3} + x_{3} \cdot y_{1}) - (y_{1} \cdot x_{2} + y_{2} \cdot x_{3} + y_{3} \cdot x_{1}) |$ $= 1/2 |(x_1*y_2 + x_2*y_3+x_3*y_1) - (y_1*x_2+y_2*x_3+y_3*x_1)|$

$= \frac{1}{2} | (5 \cdot 7 + 2 \cdot 6 + 3 \cdot 1) - (1 \cdot 2 + 7 \cdot 3 + 6 \cdot 5) |$ $= 1/2 |(5*7 + 2*6 + 3*1) - (1*2 + 7*3 + 6*5)|$

$= \frac{1}{2} | (35 + 12 + 3) - (2 + 21 + 30) |$ $= 1/2 |(35 + 12 + 3) - (2 + 21 + 30)|$

$= \frac{1}{2} | (50 - 53) | = \frac{1}{2} | (- 3) | = \frac{3}{2}$ $= 1/2 |(50- 53)| = 1/2 |(-3)| = 3/2$

Volume of pyramid = $\frac{1}{3} \cdot \frac{3}{2} \cdot 4 = 2 u n i t^{3}$ $1/3 * 3/2 * 4 = 2 unit^3$

Science

Math

Humanities

... and beyond

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?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

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 44 , what is the pyramid's volume?

1 Answer

Explanation:

Related questions

Impact of this question

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?