Area of Circle Derivation
Area of a circle can be visualized and proved using two methods, namely
- Circle Area Using Rectangles
- Circle Area Using Triangles
Circle Area Using Rectangles
Area of the Circle is derived by the method discussed below. For finding the area of a circle the diagram given below is used,
After studying the above figure carefully, we split the circle into smaller parts and arranged them in such a way that they form a parallelogram.
If the circle is divided into small and smaller parts, at last, it takes the shape of a rectangle.
Area of Rectangle = length × breadth
Comparing the length of a rectangle and the circumference of a circle we can see that,
the length is = ½ the circumference of a circle
Length of a rectangle = ½ × 2πr = πr
Breadth of a rectangle = radius of a circle = r
Area of circle = Area of rectangle = πr × r = πr2
Area of the circle = πr2
Where r is the radius of the circle.
Circle Area Using Triangles
The area of the circle can easily be calculated by using the area of triangle. For finding the area of the circle using the area of the triangle consider the following experiment.
- Let us take a circle with a radius of r and fill the circle with concentric circles till no space is left inside the circle.
- Now cut open each concentric circle and arrange them in a triangular shape such that the shortest length circle is placed at the top and the length is increased gradually.
The figure so obtained is a triangle with base 2πr and height r as shown in the figure given below,
Thus the area of the circle is given as,
A = 1/2 × base × height
A = 1/2 × (2πr) × r
A = πr2
Area of a Circle: Formula, Derivation, Examples
Area of a Circle is the measure of the two-dimensional space enclosed by a circle. It is mostly calculated by the size of the circle’s radius.
Let’s learn how to find the area of the circle using the formulas, with the help of examples.
Table of Content
- Area of Circle
- Area of Circle with Radius
- Area of Circle in terms of Diameter
- Area of a Circle using Circumference
- Area of Circle Examples