1. **State the problem:** Find the area of a regular pentagon with an apothem of 5 units. 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 pentagon, the number of sides $n = 5$. - To find the perimeter, we need the length of one side. 4. **Find the side length:** The apothem $a$ relates to the side length $s$ by the formula: $$a = \frac{s}{2 \tan(\pi/n)}$$ Rearranged to solve for $s$: $$s = 2a \tan\left(\frac{\pi}{n}\right)$$ Substitute $a=5$ and $n=5$: $$s = 2 \times 5 \times \tan\left(\frac{\pi}{5}\right) = 10 \times \tan\left(36^\circ\right)$$ Calculate $\tan(36^\circ) \approx 0.7265$: $$s \approx 10 \times 0.7265 = 7.265$$ 5. **Calculate the perimeter:** $$P = n \times s = 5 \times 7.265 = 36.325$$ 6. **Calculate the area:** $$\text{Area} = \frac{1}{2} \times P \times a = \frac{1}{2} \times 36.325 \times 5 = 90.8125$$ 7. **Round to nearest hundredth:** $$\text{Area} \approx 90.81$$ **Final answer:** The area of the regular pentagon is approximately $90.81$ square units.