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

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

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Answer 1 · 2016-04-09T12:06:55

volume $= \frac{28}{3}$ $= 28/3$

Explanation:

The volume of a pyramid is given by the formula:
$XXX V = \frac{1}{3} h b$ $color(white)("XXX")V=1/3 hb$ where $h$ $h$ is the height and $b$ $b$ is the area of the base.

We are given the height ( $h = 7$ $h=7$ )
so we need to find the base.

Method 1: Use the Pythagorean Theorem to find distance between points then apply Heron's Formula for the Area.
(left as an exercise).

Method 2: Evaluate the Area of the Triangular Base as the Sum and Difference of Trapezoids:
enter image source here
From the relationship between the triangle and the trapezoid segments we see that the area of the base of our pyramid is
$XXX b = 7 + 5 - 8 = 4$ $color(white)("XXX")b=7+5-8 =4$

Therefore the Volume of the pyramid is
$XXX V = \frac{1}{3} \times 7 \times 4 = \frac{28}{3}$ $color(white)("XXX")V=1/3 xx 7 xx 4 =28/3$

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

1 Answer

Explanation:

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The base of a triangular pyramid is a triangle with corners at (3,8)(3 ,8 ), (4,2)(4 ,2 ), and (2,6)(2 ,6 ). If the pyramid has a height of 77 , what is the pyramid's volume?

1 Answer

Explanation:

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