Arc length and sector area

A sector with angle \(\theta\) radians is the fraction \(\dfrac{\theta}{2\pi}\) of a full circle.

For an angle of \(\alpha^\circ\), the equivalent formulae are \(l=\dfrac{\alpha}{360}(2\pi r)\) and \(A=\dfrac{\alpha}{360}(\pi r^2)\).

Choosing and checking a calculation

Trace the boundary before finding a perimeter. An internal line is not part of that boundary. Use square units for area and length units for an arc or perimeter.

For a major sector, use its reflex angle. If the minor angle is \(\theta\), the major angle is \(2\pi-\theta\).

Keep exact values or full calculator precision until the final answer. Write an approximation sign when rounding. Set the calculator to the angle unit used in a trigonometric calculation.