1. The problem is to find the formula for the area of a circle. 2. The area of a circle is the amount of space enclosed within its boundary. 3. The formula for the area $A$ of a circle with radius $r$ is: $$A = \pi r^2$$ 4. Here, $\pi$ (pi) is a constant approximately equal to 3.14159. 5. This formula comes from integrating the circle's radius in all directions or by considering the circle as a polygon with infinitely many sides. 6. To use this formula, simply square the radius (multiply the radius by itself) and then multiply by $\pi$. 7. For example, if the radius is 3 units, the area is: $$A = \pi \times 3^2 = \pi \times 9 = 9\pi$$ which is approximately 28.27 square units. This formula is fundamental in geometry and is used in many applications involving circles.