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

The volume of the pyramid is

The base triangle's area is

The pyramid's volume is

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To find the volume of the triangular pyramid, you can use the formula: [ V = \frac{1}{3} \times \text{base area} \times \text{height} ]

First, you need to find the area of the base triangle using its vertices. Then, you can calculate the volume using the given height.

Using the vertices (3,4), (2,7), and (3,6) for the base triangle, you can calculate the area using the formula for the area of a triangle given its vertices.

[ \text{Area} = \frac{1}{2} \left| (x_1(y_2 - y_3)) + (x_2(y_3 - y_1)) + (x_3(y_1 - y_2)) \right| ]

Once you have the area of the base triangle, plug it into the volume formula along with the given height of the pyramid to find the volume.

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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.

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.

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.

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