How would I find the volume of a pyramid

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To find the volume of a pyramid with an equilateral triangle base, the formula is indeed 1/3 times the area of the base multiplied by the height. The area of the equilateral triangle can be calculated using the formula (sqrt(3)/4) * a^2, where 'a' is the length of a side. As the height increases, the side length of the triangle changes, influencing the area at different heights. An equation can be established for the area of a cross-section at a given height, which is essential for integrating to find the volume. Understanding these relationships is key to solving the volume calculation accurately.
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How would I find the volume of a pyramid with an equilateral triangle as it's base? I know how to do a pyramid with a square base (the integral from 0 to it's height of 2*(equation solved for y of a side)^2 dy)). Would this be the same method?
 
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Didn't your text tell you that the area of a pyramid is 1/3 the product of the area of its base and its height?
 
You can make an equation for the area of a given slice of the pyradmid with respect to the height (since the height will determine the side length, which will of course influence the area since it is equilateral..I believe it's ((a)^(3/2))/4 but I forget.
 

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