What formula is used to find the area of a circle?

The formula used to find the area of a circle is πr². This formula originates from the definition of area, which is a measure of the space inside a two-dimensional shape.

In this case, r represents the radius of the circle, which is the distance from the center of the circle to any point on its perimeter. The expression πr² indicates that the area is directly proportional to the square of the radius. This means that if the radius doubles, the area will increase by a factor of four, reflecting the quadratic relationship.

The constant π (pi) is approximately equal to 3.14159 and is crucial in calculating the area because it relates the diameter of any circle to its circumference and area. Hence, when you multiply π by the square of the radius, you effectively calculate the total space enclosed by the circle.

Understanding this formula is essential for solving problems related to circles in geometry, such as when determining the sizes of circular objects or when dealing with circular areas in real-world applications.