1. **State the problem:** Find the area of a regular hexagon with an apothem length of 6 ft, rounding to the nearest tenth. 2. **Formula for the area of a regular polygon:** $$\text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem}$$ 3. **Important rules:** - The apothem is the perpendicular distance from the center to a side. - For a regular hexagon, the number of sides $n = 6$. - Each side length $s$ can be found using the apothem and the formula $s = 2 \times \text{Apothem} \times \tan(\frac{\pi}{n})$. 4. **Calculate the side length:** $$s = 2 \times 6 \times \tan\left(\frac{\pi}{6}\right) = 12 \times \tan\left(30^\circ\right)$$ Since $\tan(30^\circ) = \frac{1}{\sqrt{3}} \approx 0.5774$, $$s = 12 \times 0.5774 = 6.9288 \text{ ft}$$ 5. **Calculate the perimeter:** $$P = n \times s = 6 \times 6.9288 = 41.5728 \text{ ft}$$ 6. **Calculate the area:** $$\text{Area} = \frac{1}{2} \times 41.5728 \times 6 = \frac{1}{2} \times 249.4368 = 124.7184 \text{ ft}^2$$ 7. **Round to the nearest tenth:** $$124.7 \text{ ft}^2$$ **Final answer:** The area of the regular hexagon is approximately **124.7 ft²**.