I’m using the Twelve Days of Christmas (and perhaps a few extra days besides) to do something that I should have done a long time ago: collect past series of posts into a single, easy-to-reference post. The following posts formed my series on different ways of finding the area of a triangle as well as finding the volumes of common shapes.
Part 1: Deriving the formula .
Part 2: Cavalieri’s principle and finding areas using calculus.
Part 3: Cavalieri’s principle and finding the volume of a pyramid and then the volume of a sphere.
Part 4: Finding the area of a triangle using the Law of Sines.
Part 5: Finding the area of a triangle using the Law of Cosines.
Part 6: Finding the area of a triangle using the triangle’s incenter.
Part 7: Finding the area of a triangle using a determinant and the coordinates of the vertices.
Part 8: Finding the area of a triangle using Pick’s theorem.
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