The original worked lessons remain the main explanations. Use these focused reminders to check the conditions before you start.
Annular sectors and composite boundaries
Combine or subtract circular and straight-edged regions.
Count only exposed edges, including both arcs of an annular sector.
Handle scaling, inverse geometry and limiting boundary cases.
An annular sector has \(A=\tfrac12(R^2-r^2)\theta\) and \(P=(R+r)\theta+2(R-r)\), for \(0<r<R\), \(0<\theta<2\pi\). A complete annulus has no radial connectors. Internal joins do not contribute to a composite perimeter. Enlargement factor \(k\) multiplies areas by \(k^2\).