Area of a sector
The area of a shape is the space contained inside it. We can find the area of a sector using the formula:
\(\frac{\texttheta}{360} \times \pi~\text{r}^{2}\)
\(\texttheta\) is the angle of the sector and \(\text{r}\) is the radius of the circle.
Example
Here, \(\text{r}\) = 11 and \(\texttheta\) = 45⁰.
Substituting these into the formula, we get:
\(\text{Area =}~\frac{45}{360} \times \pi \times {11}^{2}\)
\(\text{= 47.51...}\)
\(\text{= 47.5 cm}^{2}~\text{(to one decimal place)}\)
Question
Find the area of this sector:
\(\text{Area =}~\frac{110}{360} \times \pi \times {32}^{2}\)
\(\text{= 982.96...}\)
\(\text{= 983.0 cm}^{2}~\text{(to one decimal place)}\)