1. The problem asks to find the area of a regular pentagon with a perimeter of 50 cm. 2. Recall the formula for the area of a regular polygon: $$\text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem}$$ 3. First, find the side length of the pentagon: $$\text{Side length} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{50}{5} = 10 \text{ cm}$$ 4. To find the apothem, use the formula for a regular pentagon: $$\text{Apothem} = \frac{\text{Side length}}{2 \tan(\pi/5)} = \frac{10}{2 \tan(36^\circ)}$$ 5. Calculate $$\tan(36^\circ) \approx 0.7265$$, so $$\text{Apothem} = \frac{10}{2 \times 0.7265} = \frac{10}{1.453} \approx 6.88 \text{ cm}$$ 6. Now calculate the area: $$\text{Area} = \frac{1}{2} \times 50 \times 6.88 = 25 \times 6.88 = 172 \text{ cm}^2$$ 7. Rounded to the nearest tenth, the area is $$172.0 \text{ cm}^2$$. This corrects the earlier incorrect multiplication of perimeter and apothem.