# The base of a triangular pyramid is a triangle with corners at #(7 ,5 )#, #(3 ,2 )#, and #(5 ,7 )#. If the pyramid has a height of #8 #, what is the pyramid's volume?

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

Volume = (1/3) * base area * height

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

Then, multiply the base area by the height of the pyramid and divide by 3 to get the volume.

With the given coordinates, the area of the base triangle is 12 square units.

Volume = (1/3) * 12 * 8 = 32 cubic units.

So, the volume of the pyramid is 32 cubic units.

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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.

- Two corners of a triangle have angles of #(3 pi ) / 8 # and # pi / 12 #. If one side of the triangle has a length of #9 #, what is the longest possible perimeter of the triangle?
- A pyramid has a parallelogram shaped base and a peak directly above its center. Its base's sides have lengths of #2 # and #7 # and the pyramid's height is #6 #. If one of the base's corners has an angle of #pi/4 #, what is the pyramid's surface area?
- A circle is inscribed in a square, which means that each side of the square touches the circle at exactly one point. If the area of the circle is 144pi, what is the length of the diagonal?
- A cone has a height of #5 cm# and its base has a radius of #4 cm#. If the cone is horizontally cut into two segments #1 cm# from the base, what would the surface area of the bottom segment be?
- An ellipsoid has radii with lengths of #5 #, #5 #, and #8 #. A portion the size of a hemisphere with a radius of #3 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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