Area of a sector

The area of a sector can be calculated using the formula: $$A = \frac{x}{360} \times \frac{\text{Area of the circle}}{1} = \frac{x}{360} \times \text{π} r^2$$ , where x is the central angle in degrees and r is the radius.

'x' represents the central angle of the sector in degrees.

The area of a circle is given by the formula: $$A = \text{π} r^2$$ .

Using the formula $$A = \frac{x}{360} \times \text{π} r^2$$ , we have: $$A = \frac{90}{360} \times \text{π} \times 10^2 = \frac{1}{4} \times \text{π} \times 100 = 25\text{π} \text{ cm}^2 \text{ (approximately 78.54 cm}^2)$$ .

To convert from square centimeters to square meters, divide the area in square centimeters by 10,000.

The area of a sector is directly proportional to the central angle; as the angle increases, the area of the sector increases.

Using the formula $$A = \frac{x}{360} \times \text{π} r^2$$ , we can rearrange to find x: $$x = \frac{A \times 360}{\text{π} r^2} = \frac{15 \times 360}{\text{π} \times 5^2} \text{ (approximately 171.89 degrees)}$$ .

Using the formula $$A = \frac{x}{360} \times \text{π} r^2$$ , we have: $$A = \frac{270}{360} \times \text{π} \times 7^2 = \frac{3}{4} \times \text{π} \times 49 = \frac{147\text{π}}{4} \text{ cm}^2 \text{ (approximately 115.19 cm}^2)$$ .

Using the formula $$A = \frac{x}{360} \times \text{π} r^2$$ , we have: $$A = \frac{60}{360} \times \text{π} \times 4^2 = \frac{1}{6} \times \text{π} \times 16 = \frac{8\text{π}}{3} \text{ cm}^2 \text{ (approximately 8.38 cm}^2)$$ .

The fraction $$\frac{x}{360}$$ represents the proportion of the circle that the sector occupies, based on the central angle x.