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Why do thinner triangle result a in a larger area/ different shape?


@intelligentDungBeetle What you should imagine is that the surface with skinny triangles is a piece of paper with many small "wrinkles" in it. To make a wrinkled surface, you need a bigger piece of paper than if you want to make a smooth surface---just like you'd need a longer piece of string to make a "wobbly" curve than a straight line.