The base of a triangular pyramid is a triangle with corners at #(6 ,2 )#, #(5 ,1 )#, and #(7 ,4 )#. If the pyramid has a height of #12 #, what is the pyramid's volume?
Volume of pyramid is
Finding the base triangle's area should come first because the pyramid's volume is equal to onethird of the base area times the height.
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To find the volume of the triangular pyramid, we first need to calculate the area of the base triangle and then use it along with the height to compute the volume using the formula for the volume of a pyramid.

Calculate the area of the base triangle using the given coordinates of its vertices. You can use the formula for the area of a triangle given its vertices or use other methods such as the Shoelace formula.

Once you have the area of the base triangle, multiply it by the height of the pyramid.

Divide the result by 3 to find the volume of the triangular pyramid.
Let's go through these steps:

Calculate the area of the base triangle:
 Given vertices: ( (6, 2) ), ( (5, 1) ), and ( (7, 4) )
 Using the formula for the area of a triangle given vertices or another method, find the area of the triangle.

Multiply the area of the base triangle by the height of the pyramid:
 Height of the pyramid is given as 12 units.

Divide the result by 3 to find the volume of the triangular pyramid:
 ( \text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height} )
Once you have performed these calculations, you will obtain the volume of the triangular pyramid in cubic units.
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When evaluating a onesided 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 onesided 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 onesided 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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