Circle Area Calculation

Calculate the area of a circle using radius

The area of a circle is the product of piπ(3.1415926...) and the radius R squared, which can be expressed as: \[ Circle area \\[12pt] = \pi \times Radius^2 \\[12pt] = \pi \, R^2 \]

Calculate the area of a circle using diameter

The area of a circle can also be calculated from the diameter, which is derived from the fact that the radius is half of the diameter: \[area of a circle \\[12pt] = {\pi \,({diameter \over 2})^2} \\[12pt] = {\pi \over 4} \times diameter^2 \\[12pt] = {\pi \over 4} \, D^2 \]

Calculate the area of a circle using Perimeter

Since the circumference of a circle is the product of its diameter and pi, this relationship can be used to derive the mathematical formula for the area of a circle: \[radius = {circumference \over {2 \pi}} \] \[ Circle area \\[12pt] = {\pi \, ({circumference \over {2 \pi}})^2} \\[12pt] = {circumference^2 \over {4 \pi}} \\[12pt] = {S^2 \over {4 \pi}} \]