Prove that every triangular region is measurable and its area is one half the product of its base and altitude.(adsbygoogle = window.adsbygoogle || []).push({});

LetQbe a set that can be enclosed between two step regionsSandT, so that [tex] S \subseteq Q \subseteq T [/tex] If there is one numbercsuch that [tex] a(S) \leq c \leq a(T) [/tex], then Q is measurable, and [tex] a(Q) = c [/tex]. So we know that [tex] c = \frac{1}{2}bh [/tex]. So there has to be two step regions so that the area of the triangle is between them. We know that every rectangle is measurable, and the [tex] a(R) = bh [/tex]. So how do I prove that [tex] c = \frac{1}{2}bh [/tex]?

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# Homework Help: Apostol: Area of a triangle

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