# The base of a triangular pyramid is a triangle with corners at #(6 ,2 )#, #(4 ,5 )#, and #(8 ,7 )#. If the pyramid has a height of #6 #, what is the pyramid's volume?

Volume of pyramid is

We can find the area of the base triangle by applying Heron's formula to get the distance between the corners, which should give us three sides.

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

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

First, calculate the area of the base triangle using the formula for the area of a triangle:

Area = (1/2) * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|

Where (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the vertices of the triangle.

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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