# The base of a triangular pyramid is a triangle with corners at #(6 ,7 )#, #(3 ,1 )#, and #(5 ,9 )#. If the pyramid has a height of #8 #, what is the pyramid's volume?

Triangle Area

Slope of BC

Equation of BC

Slope of altitude through A is

Equation of altitude h is

Solving equations (1) & (2), we get the coordinates of D, the base of altitude h

#D (78/11, 128/17)

Height of altitude

Area of Triangle

Volume of Pyramid V = (1/3) * Base Area * Height

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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, find the area of the base triangle using the coordinates given for its vertices. Then, calculate the distance between the apex of the pyramid and the base plane to determine the height. Finally, substitute the values into the formula 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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