1. **Problem Statement:** Find the area of a regular hexagon with side length 10 inches. 2. **Formula:** The area $A$ of a regular polygon with $n$ sides of length $s$ can be found using the formula: $$A = \frac{1}{2} n s a$$ where $a$ is the apothem (the perpendicular distance from the center to a side). 3. **Important Rule:** For a regular hexagon, the apothem $a$ can be found using the formula: $$a = s \cos(\frac{\pi}{n})$$ Since $n=6$, $$a = 10 \cos(\frac{\pi}{6}) = 10 \times \frac{\sqrt{3}}{2} = 5\sqrt{3}$$ 4. **Calculate the area:** $$A = \frac{1}{2} \times 6 \times 10 \times 5\sqrt{3} = 3 \times 10 \times 5\sqrt{3} = 150\sqrt{3}$$ 5. **Check your work:** You wrote $360 \div 6 = 60$ which is the central angle in degrees. Then you used $10 \times 60 \times \frac{1}{2} \times 10$ which is not the correct formula for area. 6. **Correct approach:** Area of one equilateral triangle inside the hexagon is: $$\frac{1}{2} \times s \times a = \frac{1}{2} \times 10 \times 5\sqrt{3} = 25\sqrt{3}$$ Since there are 6 such triangles, $$6 \times 25\sqrt{3} = 150\sqrt{3}$$ 7. **Final answer:** $$\boxed{150\sqrt{3} \text{ in}^2}$$ Your answer of 300 in² is not exact and does not use the apothem correctly. The exact area is $150\sqrt{3}$ in².