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How to Find the Area of a Circle?

Area of Circle

In mathematics, a circle is a set of points in a plane that are all the same distance from a central point. Coins, dinner plates, pizza, and other items are only a few examples of circles in the real world. Radius is the distance between the center and the points. The diameter is half of the radius of the circle.  The circle is a closed 2D object made up of equidistant points around a central point. The term “circle” comes from the Greek word “kirkos,” which means “ring.”  In this article, we have discussed the properties of a circle, the definition of a circle, and the Area of Circle

Area of Circle Formula

A circle is a locus of a point moving around a fixed point at a fixed distance away from the point. A circle is a closed curve with an exterior line equidistant from the center(Interior fixed point). The radius of the circle is the fixed distance from the fixed point(also called the center of the circle). Many examples of the circle can be found in everyday life, such as the sun, ball, and round playground, and so on.

Area of Circle Using circumference

Now we know the definition of the circle with real-time examples. Let’s know the parts of the circle. The following parts of the circle are given below, before knowing the formula of the circle one must know the parts of the circle for a better understanding of the circle formula.
Area of Circle = C*C/4*pi, where C is Circumference

Area of Circle Using Diameter

Diameter of circle: The circle’s diameter is the line that divides the circle into two equal sections or we can say, it is just the double of the radius of the circle, and is denoted by the letters ‘d’ or ‘D’.

D= R/2

Where,

D= Diameter of the circle

R = Radius of the circle

If the radius is given then we can find the diameter of the circle by using the formula given above.

Radius of the circle: A radius is a distance between the circle’s center and any point on it. when two radii are placed on top of each other, the resultant has the same length as one diameter. As a result, one diameter is twice the radius.

Chord: The chord is a segment of a line that joins two points on a curve. The use of a chord in geometry is focused on describing a line segment connecting two endpoints that rest on a circle.

Three Ways to calculate the Area of the Circle

Calculating the area of a circle based on given information is a popular problem in geometry class. The basic formula to calculate the area of the circle is A = π2, where r is the radius of the circle. This formula we have been using since school. Here we have given the three methods to calculate the area of the circle.

Using a radius to find an Area of the Circle

The radius of a circle is the distance between its center and its periphery. The radius will be the same regardless of which way you measure it. A circle’s radius is also twice its diameter. In most cases, you will be given a radius. If the center of the circle is not marked then it will be difficult to find the radius of the circle.

Let us assume that the radius of the circle is 14 cm

A = πr2

Use this formula to find the area of the circle, we have given that the radius of the circle is 14 cm. And we know that the value of π is 22/7 put these values is in the given formula to calculate the area of the circle.

A = 22/7*14*14

A= 616 Cm2

Using the Diameter to Calculate the Area

If the diameter is given then it’s easy to calculate the area of the circle. We have learned that diameter is twice the radius, if the radius is given then it’s easy to find the area of the circle.

A = πr2

We can put  radius = 2* diameter

A = π(2d)2

Example: Assume that the diameter of the circle is 28cm, then find the area of the circle.

Solution: We know that the value of π is 22/7 and it’s unitless, and we have given the diameter of a circle which is 28cm.

A = 22/7(2*28)2

A = 9856 cm2

We have got the area of the circle which is A = 9856 cm2

Using Circumference to calculate the area of a circle

Here we have given the method to calculate the area of the circle using the circumference of the circle. If the radius of a circle and diameter of the circle is not given and only circumference is given then we can use the formula given below to find the area of the circle.

A = C2/4π

Example: Assume the circumference of the circle is 7cm

Solution: We have given the circumference of the circle, so we will use the formula given above to find the area of the circle.

A = C2/4π

A = 7*7/4*(22/7)

A = 3.89 cm2

We have got the area of the circle is A = 3.89 cm2

Hence, we have covered the three ways to calculate the area of the circle. The students must use all three methods to calculate the area of the circle. To ease of students we have provided the examples, students must refer to the examples and practice as much as they can.

FAQs on Area of the Circle

Q. How to calculate the area of the circle?

If the radius is given then we can use A = πr2 to calculate the area of the circle. The other methods to calculate the area of the circle are given on this page.

Q. What is the definition of a circle?

A circle is a locus of a point moving around a fixed point at a fixed distance away from the point.

Q. What are the parts of a circle?

The parts of the circle include radius, diameter, and circumference.

Q. How to find the area of a circle when the circumference is given?

We can use A = C2/4π to calculate the area of a circle when the circumference is given.

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