Areas of curved figures

Curved figures include circles, ellipses, sectors, segments, and regions bounded by curves. Their areas are calculated using formulas derived from geometry, often involving $ext{π}$ and the properties of the figure (like radius or angle).

Important properties

• The area of a circle is $A = ext{π} r^2$.

• The area of a sector of a circle with central angle $heta$ (in degrees) is $A = \frac{\theta}{360} \pi r^2$.

• The area of a segment (a 'slice' cut off by a chord) can be found by subtracting the area of the triangle from the area of the sector.

• Areas of more complex curved figures may require breaking them into simpler parts or using symmetry.