To calculate the area of a circle, you can use the formula:

The area of a circle represents the space enclosed within its boundary. To determine this area, you need to know the radius, which is the distance from the center of the circle to any point on its circumference. The area is computed by multiplying $\pi$ (pi) by the square of the radius. The constant $\pi$ is a special mathematical value approximately equal to $3.14159$. For most GCSE Mathematics problems, you can use the rounded value of $3.14$ or the $\pi$ button available on your calculator.

For instance, if the radius of a circle is $5 \, \text{cm}$, you would first calculate the square of the radius:

Next, multiply this result by $\pi$:

Thus, the area of the circle is approximately $78.5 \, \text{cm}^2$.

It’s important to remember that the radius is half of the diameter. Therefore, if the diameter is given, simply divide it by $2$ to find the radius before applying the formula. For example, if the diameter is $10 \, \text{cm}$, the radius would be:

You can then proceed with the area calculation as described earlier.

Understanding this formula is essential for solving a wide range of problems in geometry and practical applications, such as calculating the area of circular gardens, pizzas, or other round objects. Practicing with different values will enhance your confidence and proficiency in these calculations.