## How to find Area of a CircleIn this section, we will learn how to find the area of a circle. At the last of this section, we have explained some examples related to the area of a circle with different scenario for better understanding.
A circle has the following components: **Origin:**It is a point that lies exactly at the center of a circle is called the**origin**. It is denoted by**o**.**Radius:**The distance from the radius to circumference is called the**radius**. In other words, it is**half**of the diameter. It is denoted by**r**.**r=d/2****Diameter:**It is the length of a line that splits a circle into two equal parts is called the**diameter**. The line should be passed through the center. In other words, the diameter is**twice**the radius of a circle. It is denoted by**d**.**d = 2r****Chord:**The line whose endpoints lie on the circle is called a**chord**. In other words, it is a line that joins two points on any curve. Every diameter is a chord. But not every chord is a diameter. In the following figure, the line segment**AB**is a chord.**Circumference:**The reign covered by the circle is called the**circumference**. It is denoted by**C**.**C = πd or C = 2πr** Where π is a constant whose value is 3.1415.
## DefinitionThe reign occupied by a circle in the 2D plane is called the In the following figure, the colored area represents the area of the circle. ## Area of Circle FormulaA = πr^{2}Where,
## Derivation of Area of CircleThere are two methods for deriving the area of circle formula: - Using rectangles
- Using triangles
## Using RectanglesDraw a circle and divide it into The area of parallelogram-shaped will be equal to the area of a circle because each part has the same area and equal arc length. The green color parts represent half of the circumference, and the other part in red color represents the other half circumference. If the number of parts increased, the parallelogram-shape looks like a rectangle whose length is equal to We know that, The area of a rectangle (A) = w * l Where w is the width, and l is the length of the rectangle. From the figure, width (w) = πr and length (l) = r putting these values in the formula, we get area (A) = πr * r Hence, A = πr^{2}## Using TriangleDraw a circle with radius r. In this circle, draw some other concentric circles (the circle that has the same center), as shown in The base and height of the triangle will be equal to the circumference and radius of the circle, respectively. When we calculate the area of a triangle, it gives the area of a circle as a result. We know that: Area of triangle (A) = ½*base*height From the above figure, base = 2πr and height= r Put the value of base and height in the area of triangle formula, A = 1/2 * (2πr) * r Hence, A = πr^{2}## Examples
We have given, diameter (d) = 15 cm. Area =? First, we will find the radius. We know that,
From the above formula, r = d/2r = 15/2 = 7.5We know that, area of circle (A) = πr^{2}A = 3.14 * (7.5*7.5) A = 3.14 * 56.25 A = 176.625 sq cm.
We have given, radius (r) = 10 cm. Area =? We know that,
putting the value of r in the above formula, A = 3.14 * (10*10) A = 3.14 * 100
Given, circumference (C) = 20 cm Area =? We know that,
From the above formula, 20 = 2* 3.14 * r r = 20 / 2 * 3.14 r = 10 * 3.14 = 31.40 we know that,
A = 3.14 * (31.40 * 31.40) A = 3.14 * 985.96
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