For concentric sectors of radii R>r and common angle theta, subtract the smaller sector: A= 12(R2-r2)theta. The boundary has two arcs and two radial edges: P=Rtheta+rtheta+2(R-r). Mark the boundary before adding lengths; internal construction lines are not perimeter. Here R=6, r=3, theta= 3, giving A= 92pi cm2 and P=(3pi+6) cm. For any compound figure, identify the included sectors and triangles, calculate with consistent units and radians, then add or subtract the relevant areas. Keep exact values until a decimal is requested.

For concentric sectors of radii \(R>r\) and common angle \(\theta\), subtract the smaller sector: \(A=\dfrac12(R^2-r^2)\theta\).

The boundary has two arcs and two radial edges: \(P=R\theta+r\theta+2(R-r)\). Mark the boundary before adding lengths; internal construction lines are not perimeter.

Here \(R=6\), \(r=3\), \(\theta=\dfrac\pi3\), giving \(A=\dfrac92\pi\text{ cm}^2\) and \(P=(3\pi+6)\text{ cm}\).

For any compound figure, identify the included sectors and triangles, calculate with consistent units and radians, then add or subtract the relevant areas. Keep exact values until a decimal is requested.

Compound circular regions

Compound circular regions