Perimeter and Area of a Circle — A Review

Recall that the distance covered by travelling once around a circle is its perimeter, usually called its circumference. You also know from your earlier classes, that circumference of a circle bears a constant ratio with its diameter. This constant ratio is denoted by the Greek letter π (read as ‘pi’).

Before we go into details, let us see if we understand the standard terminology of circles. Though we know that pi is approximately 3.14, what does it mean visually. How does it relate to circles.

Consider a circle whose diameter is 1 unit. That is d = 2 * r = 1 unit. The circumference or perimeter of a circle is nothing but someone walking around the circle. It can be visualized as unrolling a circle as below.

As you can see, a circle whose diameter is 1 has a circumference of π. Similarly a circle whose diameter is 2 will have a circumference of 2π3ππ.

So a circle with a diameter of d will have a circumference of π3π2π * d.

π is an irrational number and its decimal expansion is non-terminating and non-recurring (non-repeating). However, for practical purposes, we generally take the value of π as 227 or , approximately.

Another way to look at the circumference of a circle is as below. We know that the angle made by an arc of a circle with the same length as its radius is 1 . Visually we can represent it as below.

Continue

As you can see, if we take the radius of the circle and bend it over the circle and traverse the circle, to cover half the circle we travel approximately 3.14 *r or π *r and to travel the whole circle we travel 2π * r distance.

Area circle

The Area of a Circle

But how do we actually calculate the area of a circle? Let’s try the same technique we used for finding the area of quadrilaterals: we cut the shape into multiple different parts, and then rearrange them into a different shape we already know the area of (e.g. a rectangle or a triangle).

The only difference is that, because circles are curved, we have to use some approximations: