What is the formula for the area of a circle?

The formula for the area of a circle is \( A = \pi r^2 \).

To understand this formula, let's break it down. The symbol \( A \) represents the area of the circle, which is the amount of space inside the circle's boundary. The Greek letter \( \pi \) (pi) is a mathematical constant approximately equal to 3.14159. It represents the ratio of the circumference of any circle to its diameter. The letter \( r \) stands for the radius of the circle, which is the distance from the centre of the circle to any point on its edge.

The formula \( A = \pi r^2 \) tells us that to find the area, we need to square the radius (multiply the radius by itself) and then multiply the result by \( \pi \). For example, if the radius of a circle is 3 cm, the area would be calculated as follows: \( A = \pi \times 3^2 = \pi \times 9 \approx 28.27 \) square centimetres.

This formula is derived from the relationship between the circle's radius and its circumference. By dividing a circle into many small sectors (like slices of a pie) and rearranging them, we can approximate the shape of a parallelogram. The area of this parallelogram is similar to the area of the circle, leading to the formula \( A = \pi r^2 \). Understanding this formula is crucial for solving various problems in geometry and real-life applications, such as finding the area of circular gardens, pizzas, or any round objects.