1. **State the problem:** Find the area of a circle given its radius. 2. **Formula:** The area $A$ of a circle with radius $r$ is given by the formula: $$A = \pi r^2$$ 3. **Explanation:** This formula comes from the definition of a circle and the constant $\pi$ which relates the circumference and diameter. 4. **Example:** If the radius $r$ is known, substitute it into the formula. 5. **Intermediate step:** For example, if $r=5$, then: $$A = \pi \times 5^2 = \pi \times 25$$ 6. **Final answer:** $$A = 25\pi$$ This is the exact area of the circle in terms of $\pi$.