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

Answer 1

volume #= 28/3#

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

We are given the height (#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:
Therefore the Volume of the pyramid is
#color(white)("XXX")V=1/3 xx 7 xx 4 =28/3#

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Answer 2

Allison Allen

The volume of the triangular pyramid is ( \frac{1}{3} \times \text{base area} \times \text{height} ). Given the coordinates of the triangle's corners, the base area can be calculated using the formula for the area of a triangle. Then, substituting the base area and the given height into the formula for the volume of a pyramid will yield the result. The volume of the pyramid is approximately ( \frac{105}{2} ) cubic units.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.