## Area of a Circle

Circle is one of the basic polygons in Geometry. Circle is a polygon or a shape which is a closed curve that divides the plane into 2 regions. A Circle is a plane bounded by one line and the lines which are drawn from the centre to the bounded line are equal.

#### Area of Circle:

To find the area of the Circle there is a formula which was proved by the Archimedes.

Area of circle when we know the radius

**Area of a circle ****A = ****πr ^{2 }**

^{}There is other formula to find the area of the circle when we know the diameter

Area of a circle **A = ****π****/4 * D ^{2}**

There is one formula to find the area of the circle when we know the Circumference

Area of a circle **A = C ^{2}/4**

**π**

Let us know how to find the area of the circle when we know the radius

Examples:

#### Find the Area of the Circle whose radius is 6m?

Here in this example we know the radius of the circle so we can apply the first formula

**Solution:**

Area of a circle A = πr^{2}^{ }^{}

A – Area of the circle we have to find

π – pi – ( the value of π is 3.14159)

r- radius of the circle = 6

Now substitute the values in the formula

A = **πr ^{2}**

A = 3.14159 * 6^{2}

A = 3.14159 * 6*6

A= 3.14159 * 36

**A = 113.09733**

#### Find the Area of the Circle whose diameter is 3m?

Here in this example we know the diameter of the circle so we can apply the second formula

**Solution:**

Area of a circle A = π/4 * D^{2}

A – Area of the circle we have to find

π – pi – ( the value of π is 3.14159)

D- Diameter of the circle = 3

Now substitute the values in the formula

A = π/4 * D^{2}

A = 3.14159/4 * 3^{2}

A = 0.78539 * 3*3

A= 0.78539 * 9

**A = 7.06858**

#### Find the Area of the Circle whose Circumference is 6m?

Here in this example we know the circumference of the circle so we can apply the third formula

**Solution:**

Area of a circle A = C^{2}/4π

A – Area of the circle we have to find

π – pi – ( the value of π is 3.14159)

C- Circumference of the circle = 6

Now substitute the values in the formula

A = C^{2}/4π

A = 6^{2}/4*3.14159

A = 6*6/4*3.14159

A= 36/12.56637

**A = 28.2743**

#### What is Radius of a Circle?

As we know Circle is a plane bounded by one line and the lines which are drawn from the centre to the bounded line are equal.

Radius is the distance calculated from the centre of the circle to the bounded line

#### What is the Diameter of a Circle?

Diameter is the line goes across the circle through the centre of the circle

**Diameter of a Circle = 2 * Radius of the Circle**

#### What is the Circumference of a Circle?

Circumference is the distance calculated around the circle

**Circumference of a Circle = ****π *
Diameter **or

**Circumference of a Circle = 2πr**

#### What is π?

**π or pi = Circumference of the circle / Diameter of the
Circle**

The Value of π = 3.1459