Area of Circle/Proof 3/Lemma 1

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Lemma for Area of Circle: Proof 3


Construct a circle with radius $r$ and circumference $c$, whose area is denoted by $C$.

Construct a triangle with height $r$ and base $c$, whose area is denoted by $T$.


$T = \pi r^2$


\(\ds T\) \(=\) \(\ds \frac {r c} 2\) Area of Triangle in Terms of Side and Altitude
\(\ds \) \(=\) \(\ds \frac {r 2 \pi r} 2\) Perimeter of Circle
\(\ds \) \(=\) \(\ds \pi r^2\)