How do you calculate the area of a sector?

To calculate the area of a sector, use the formula: \(\text{Area} = \frac{\theta}{360} \times \pi r^2\).

A sector is a portion of a circle, resembling a 'slice of pie'. The formula for the area of a sector involves the central angle (\(\theta\)) in degrees and the radius (\(r\)) of the circle. The central angle is the angle formed at the centre of the circle by the two radii that define the sector.

Here's how the formula works: \(\frac{\theta}{360}\) represents the fraction of the circle that the sector occupies. Since a full circle is 360 degrees, dividing the central angle by 360 gives you the proportion of the circle that the sector represents. Multiplying this fraction by the area of the entire circle (\(\pi r^2\)) gives you the area of the sector.

For example, if you have a sector with a central angle of 90 degrees and a radius of 5 cm, you would substitute these values into the formula:

\[
\text{Area} = \frac{90}{360} \times \pi \times 5^2
\]

Simplify the fraction:

\[
\text{Area} = \frac{1}{4} \times \pi \times 25
\]

Then multiply:

\[
\text{Area} = \frac{25\pi}{4} \approx 19.63 \text{ cm}^2
\]

So, the area of the sector is approximately 19.63 square centimetres. Remember to always use the same units for the radius and to convert the angle to degrees if it’s given in another unit.