# Area of a Circle Using its Radius

To find the area of a circle, we need to know its radius. The radius is the distance from the center of the circle to any point on its perimeter. If we let \( r \) represent the radius, the area \( A \) can be calculated using the formula \( A = \pi r^2 \).

**Example 1:** Find the area of the circle below.

To calculate the area of the circle, we will use the formula \(A = \pi {r^2}\). This requires determining the radius of the circle. Observing the circle drawn on the grid, we see that the distance from the center to the edge (or perimeter) of the circle is \(3\) units. This is because there are \(3\) squares between the center and the edge.

Since \(r=3\), the area of the circle is

$$\eqalign{

A &= \pi {r^2} \cr

& = \pi {\left( 3 \right)^2} \cr

& = 9\pi \cr} $$

Therefore, the area of the circle is \(9\pi\) \(\text{unit}^2\).

**Example 2:** Calculate the area of a circle with a diameter of \(14\) \(\text{in}\).

Remember that the diameter of a circle is the distance between any two points on the circle that passes through the center. The diameter’s length is twice that of the radius. If we denote the diameter as \(d\) and the radius as \(r\), we can represent their relationship with the equation \(d = 2r\).

It implies that to determine the radius when the diameter is given, we just need to divide the diameter by \(2\). Thus,

$$r = {d \over 2} = {{14} \over 2} = 7$$

The area of a circle with a radius of 7 inches is calculated as follows.

$$\eqalign{

A &= \pi {r^2} \cr

& = \pi {\left( 7 \right)^2} \cr

& = 49\pi \cr} $$

Therefore, the area of the circle is \(49\pi \) \(\text{in}^2\).