# The base of a triangular pyramid is a triangle with corners at #(3 ,4 )#, #(2 ,9 )#, and #(5 ,7 )#. If the pyramid has a height of #7 #, what is the pyramid's volume?

Given

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The volume of the pyramid is provided by

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To find the volume of a triangular pyramid, you can use the formula:

[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} ]

First, calculate the area of the base triangle using the given coordinates. You can use the formula for the area of a triangle given its vertices:

[ A = \frac{1}{2} \times |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)| ]

Then, multiply the area of the base triangle by the height of the pyramid, and divide the result by 3 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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