Short answer: a 90° sector of a radius-2 circle has area π ≈ 3.1416, arc length π ≈ 3.1416 and chord 2√2 ≈ 2.8284. Area and arc both come out at π here because r = 2 and θ = π/2 cancel neatly.
Degrees versus radians
In degrees the area is θ over 360 times πr². In radians the same thing is ½r²θ. Both give the same answer — the radian form is shorter only after the conversion, and that is the step worth seeing rather than skipping.
Worked example
A windscreen wiper of length 60 cm sweeping 120° clears ½ × 0.6² × (2π/3) = 0.377 m². Its tip travels an arc of 0.6 × 2.094 = 1.257 m, which is how the swept length is measured on a test bench.