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## 'Weekly Challenge 23: Stand up Arcs' printed from http://nrich.maths.org/

The triangle made up of the stand up arcs has area
$\frac{1}{2}\times r \times \frac{1}{2}\pi r$ which is
$\frac{1}{4} \pi r^2$. This is equal to the area of a quarter of
the unit disc so the unit disc has area $\pi r^2$.

Suppose you straightened complete circuar arcs.Then the tops would
lie on the line $y = 2 \pi x$ and the area of the triangle made
from these stand up arcs would be $\frac{1}{2}\times r \times2
\pi r$ which is $\pi r^2$. This gives the area of the whole unit
disc.