1. **State the problem:** Find the area of a regular pentagon with an apothem (distance from center to a side) of 19 m. 2. **Formula:** The area $A$ of a regular polygon is given by $$A = \frac{1}{2} \times P \times a$$ where $P$ is the perimeter and $a$ is the apothem. 3. **Important rules:** - A regular pentagon has 5 equal sides. - The apothem is perpendicular to each side and helps calculate the area. 4. **Find the side length:** The apothem $a$ relates to the side length $s$ by $$a = \frac{s}{2 \tan(\pi/5)}$$ Rearranged, $$s = 2a \tan(\pi/5)$$ Substitute $a=19$: $$s = 2 \times 19 \times \tan(36^\circ)$$ Calculate $\tan(36^\circ) \approx 0.7265$: $$s = 38 \times 0.7265 = 27.607$$ 5. **Calculate perimeter:** $$P = 5 \times s = 5 \times 27.607 = 138.035$$ 6. **Calculate area:** $$A = \frac{1}{2} \times P \times a = \frac{1}{2} \times 138.035 \times 19$$ $$A = 69.0175 \times 19 = 1311.3325$$ 7. **Round to nearest hundredths:** $$\boxed{1311.33 \text{ m}^2}$$ This is the area of the regular pentagon with apothem 19 m.