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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?

Answer 1

Caroline Aucoin

#V=56/3#.

The surface of a triangle with vertices #(0,0),(x_1,y_1)# and #(x_2,y_2)# is #S=1/2abs(x_1y_2-x_2y_1)#.

Therefore, the surface of the base is #S=1/2abs((7-3)(5-7)-(7-5)(5-2))=7#.

The volume is #V=1/3*7*8=56/3#.

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Answer 2

Allison Allen

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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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.