![]() This will aid in identifying the three parts I alluded to above. The lines of the three edges are given by:įind the intersections of each of the two planes with those three lines (so you should end up with two sets of three points). ![]() Using the base area found from the three points and the orientation/intersection points of the two planes and the prism, you can find the height of the "middle" prism and the heights of the two pyramids and thus find the total volume. ![]() I suspect by the wording that the two planes do not intersect inside of the prism (otherwise the wording is poor and this is a more difficult problem).Īssuming the planes do not intersect inside of the prism, then you can break the region into three parts: 1) a right triangular prism, and 2) and 3) two pyramids on each "tip". Solution: Given, base length b 5 inches, the height h 3 inches, and length between the triangular bases l 8. Then you need to find where the planes intersect the triangular prism. Example 1: Find the volume of a triangular prism that has the following dimensions: base length of the triangle 5 inches, the height of the triangle 3 inches, and length of the prism 8 inches. You need to find the area of the base (the triangle), this can be found from the three coordinates given using something like Heron's Formula (I don't know if that triangle permits an easier way or not-it would appear the triangle given is a right triangle). I don't necessarily see this as a calculus problem-more of a geometry problem (although I understand the calculus tag since vectors/planes tend to be taught in Cal-II or Cal-III). The formula for the volume of a prism where (A) is the area of the cross section and (h) is the height/length of the solid is: V Ah Example This shape is a triangular prism so.
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