# Area Of A Circle Formula

## Area of a Circle Formula

A circle is a rounded shape made up of points that are equally spaced apart from one another and its center. The centre of the circle is the location from which the radius is calculated. The distance between any two points on a circle’s surface and its centre is its radius. The length of one diameter would be equal to two radii placed end to end in a circle. Modern mathematics can calculate the area using integral calculus or its more complex descendant, real analysis.As a result, a circle’s diameter is twice as long as its radius. The number of square units contained within a circle is its area.  A circle has the largest area for a given perimeter and the smallest area for a given perimeter. The circumference of a circle is equal to its perimeter C. Every geometrical shape has a defined area. The region that the shape occupies in a 2D plane is what this area is known as. When discussing a circle’s Area Of A Circle Formula, one has to refer to the area on a 2D plane that is completely covered by the circle’s radius. The formula that can be used to determine the circle’s area is the Area Of A Circle Formula.

## What is a Circle

All points in a plane that are at a specific distance from a specific point, called the centre, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

The radius of a circle is the distance between any two points on the circle and its centre. The radius must typically be a positive integer.

### Diameter

Diameter is the length of a line segment whose endpoints are on the circle and which passes through its centre. The maximum distance exists between any two locations on the circle at this time. It is a unique instance of a chord, specifically the longest chord for a particular circle, and its length is double the radius. The diameter of a circle is equal to the length of the rope that encircles it.

### Area of a Circle Definition

In geometry, the Area of A Circle Formula is equal to r2 when surrounded by a circle of radius r.Here, the Greek letter ℼ stands for the constant proportion of a circle’s circumference to its diameter, which is roughly equivalent to 3.14159. This Area Of A Circle Formula, which was first discovered by Archimedes, can be derived by considering the circle as the boundary of a series of regular polygons. The method for calculating a regular polygon’s area reads “the area is half the perimeter times the radius.” For a circle, it reads “the area is half the perimeter times the distance from the centre to the sides.”

### Circumference of A Circle

The circumference of a circle is the total distance travelled in making one full turn around it. The complete length of a closed figure’s boundary is referred to as the figure’s perimeter. The perimeter has a distinct name when it comes to circles. It is referred to as the circle’s “circumference.” The whole length of the circle’s boundary is known as its circumference. The circumference of a circle can be found by opening it up and drawing a straight line; this yields the length of the circle.

### Solved Example

Solved examples on the Area Of A Circle Formula are available on the Extramarks website as well as the mobile application.