To recall, the area is the region that populated the shape in a two-dimensional plane. In this article, friend will learn the area of a circle and also the formulas because that calculating the area that a circle.

You are watching: What is the area of a circle with a diameter of 6 inches?

What is the Area the a Circle?

The area the the one is the measure up of the room or an ar enclosed within the circle. In basic words, the area the a one is the total number of square systems inside that circle.

For example, if you draw squares of dimensions 1cm by 1cm within a circle. Then, the total variety of full squares located inside the circle to represent the area of the circle. We have the right to measure the area the a one in m2, km2, in2, mm2, etc.

Formula for the Area that a Circle

The area that a circle have the right to be calculated using 3 formulas. This formulas are used depending top top the details you are given.

Let us talk about these formulas for finding the area the a circle.

Area that a circle utilizing the radius

Given the radius that a circle, the formula because that calculating the area of a circle states that:

Area the a one = πr2 square units

A = πr2 square units



Given the diameter,

A = πd2/4 square units

= 3.14 x 502/4

= (3.14 x 50 x 50)/4

=1962.5 cm2

Example 7

Calculate the area that a dinner plate, which has actually a diameter that 10 cm.


A = πd2/4 square units

= 3.14 x 102/4

= (3.14 x 10 x 10)/4

= 78.5 cm2

Example 8

The diameter that a circular plate is 20 cm. Find the size of a square plate that will have the exact same area as the circular plate.


Equate the area that the circle to the area that the square

πd2/4 = s2

3.14 x 202/4 = s2

s2 =314

Find the square source of both political parties to get,

s = 17.72

Therefore, the dimensions of the square plate will certainly be 17.72 centimeter by 17.72 cm.

Example 9

Find the diameter that a circle v an area the 156 m2.


A = πd2/4

156 = 3.14d2/4

Multiply both sides by 4.

624 = 3.14d2

Divide both sides by 3.14.

198.726 = d2

d = 14.1 m

Thus, the diameter of the circle will be 14.1 m.

See more: What Does God Helps Them That Help Themselves Meaning, God Helps Those Who Help Themselves

Area of a circle using the circumference

As we already know, the circumference of a circle is the distance about a circle. That is possible to calculation the area the a circle given its circumference.