Subjects geometry

Area Coverage C85C52

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **State the problem:** Desiree needs to find the total area to cover with stone pavers, which includes the patio and the walkway. 2. **Identify the shapes and dimensions:** - Walkway: A rectangle 12 feet wide. - Patio: A hexagonal shape with given side lengths. 3. **Calculate the area of the walkway:** The walkway is 12 feet wide and extends along the patio. The problem states the walkway is rectangular with dimensions 30 ft (bottom edge) and 25 ft (top edge), and 13 ft vertically on the right side. Since the width is consistent at 12 ft, we consider the length as the average of the two horizontal edges: $$\text{Length} = \frac{30 + 25}{2} = \frac{55}{2} = 27.5 \text{ ft}$$ Area of walkway: $$A_{walkway} = \text{width} \times \text{length} = 12 \times 27.5 = 330 \text{ ft}^2$$ 4. **Calculate the area of the patio:** The patio is a hexagon with sides mostly 13 ft and one side 26 ft. We can split the hexagon into simpler shapes or use the given dimensions 24 ft (top to bottom) and 23 ft (across) to approximate the area as a rectangle: $$A_{patio} = 24 \times 23 = 552 \text{ ft}^2$$ 5. **Calculate total area:** $$A_{total} = A_{walkway} + A_{patio} = 330 + 552 = 882 \text{ ft}^2$$ 6. **Answer:** Desiree needs to cover **882** square feet with stone pavers.