A compound circular figure combines sectors or semicircles with straight-sided shapes. Area follows the regions included; perimeter follows only the exposed boundary. First split the region at a useful radius or diameter. Write each added or removed area. Trace the outside once, omitting every shared internal edge, then add the exposed lengths. In the diagram, a semicircle of diameter 4 cm is attached outside a 7 cm by 4 cm rectangle. The area is 7(4)+ 12pi(22)=28+2pi cm2. The outside boundary is 7+7+4+2pi=18+2pi cm. The shared diameter is internal, so it contributes no perimeter. A cut-out uses subtraction for area but its exposed curved edge still contributes positively to perimeter. Exam check: keep exact values until the last step. If materials come in whole bags or rolls, round the number of units up, not the measured area or length down.

A compound circular figure combines sectors or semicircles with straight-sided shapes. Area follows the regions included; perimeter follows only the exposed boundary.

First split the region at a useful radius or diameter. Write each added or removed area. Trace the outside once, omitting every shared internal edge, then add the exposed lengths.

In the diagram, a semicircle of diameter \(4\text{ cm}\) is attached outside a \(7\text{ cm}\) by \(4\text{ cm}\) rectangle. The area is \(7(4)+\frac12\pi(2^2)=28+2\pi\text{ cm}^2\). The outside boundary is \(7+7+4+2\pi=18+2\pi\text{ cm}\).

The shared diameter is internal, so it contributes no perimeter. A cut-out uses subtraction for area but its exposed curved edge still contributes positively to perimeter.

Exam check: keep exact values until the last step. If materials come in whole bags or rolls, round the number of units up, not the measured area or length down.

Compound circular areas and exposed boundaries

Compound circular areas and exposed boundaries