Sector area and angle from the arc length

Text

A circular sector has arc length $10$ cm and radius $8$ cm. Find the area of the sector and the central angle in radians.

Solution

The area of a sector can be written as $\mathcal A=\dfrac12\,r\,L$: $\mathcal A=\frac12\cdot8\cdot10=40\ \text{cm}^2.$ The central angle in radians is $\theta=\dfrac{L}{r}$: $\theta=\frac{10}{8}=1.25\ \text{rad}.$ $\boxed{\mathcal A=40\ \text{cm}^2;\ \ \theta=1.25\ \text{rad}}$