1. **Problem Statement:** Find the area of an equilateral triangle with side length $10$ cm. 2. **Formula:** The area $A$ of an equilateral triangle with side length $s$ is given by: $$A = \frac{\sqrt{3}}{4} s^2$$ This formula comes from the fact that all sides are equal and the height can be found using the Pythagorean theorem. 3. **Calculation:** Substitute $s = 10$ cm into the formula: $$A = \frac{\sqrt{3}}{4} \times 10^2 = \frac{\sqrt{3}}{4} \times 100$$ 4. **Simplify:** $$A = 25\sqrt{3}$$ 5. **Final Answer:** The area of the equilateral triangle is: $$25\sqrt{3} \text{ cm}^2$$ This is approximately $43.3$ cm$^2$ if you want a decimal value.