The circle below has center O,
and ∠ AOB = 90°. That is a quarter of a circle.
AB has arc length 2π units, Ok so the circumference must be 8pi
\(2\pi r=8\pi\\ so\\ r=4\;units\\~\\ Area = \frac{1}{4}*\pi r^2\\ Area = \frac{1}{4}*\pi *4^2\\ Area =4\pi\;\;units^2\)
