The area of the walkway is the area of the full circle with radius \(5r\) minus the area of the pond:
["Title: How to Calculate the Walkway Area Around a Circular Pond: A Step-by-Step Guide", "When designing or planning a landscaped space, one common task is determining the usable walkway area surrounding a central circular pond. If your walkway is shaped as a full circular ring with an outer radius of (5r) and a central pond having radius (r), the formula to calculate the walkway area becomes both practical and mathematically elegant.", "In this article, we explore how to compute the walkway area by subtracting the area of the pond from the total circular walkway region — a classic problem in geometry with real-world applications in landscape architecture and garden design.", "---", "### Understanding the Geometry", "Imagine a full circle representing the total walkway area, with an outer radius of (5r). This circle fully encloses a central circular pond of radius (r) — the part you do not intend to walk on. The walkway area lies strictly in the annular (ring-shaped) region between the outer edge and the pond.", "---", "### Formula for the Walkway Area", "The area of a circle is calculated using:", "[\n\ ext{Area} = \pi \ imes (\ ext{radius})^2\n]", "Thus:", "- Area of the full circular walkway region (outer circle):", "[\nA_{\ ext{outer}} = \pi (5r)^2 = 25\pi r^2\n]", "- Area of the central pond (inner circle):", "[\nA_{\ ext{inner}} = \pi r^2\n]", "- Area of the walkway (the ring-shaped region):", "[\nA_{\ ext{walkway}} = A_{\ ext{outer}} - A_{\ ext{inner}} = 25\pi r^2 - \pi r^2 = 24\pi r^2\n]", "---", "### Step-by-Step Calculation", "1. Identify the outer radius: (R = 5r)\n2. Identify the inner radius (pond radius): (r)\n3. Compute outer area: (25\pi r^2)\n4. Compute inner area: (\pi r^2)\n5. Subtract inner area from outer area:\n[\nA_{\ ext{walkway}} = 25\pi r^2 - \pi r^2 = 24\pi r^2\n]", "---", "### Real-World Implication", "This calculation helps landscape designers and homeowners estimate materials like walkway paving, gravel, or decorative stones needed for the border area, excluding the frequently flat or natural surface occupied by the pond. Knowing the walkway’s usable area ensures efficient resource use and helps avoid overestimating or underestimating installation needs.", "---", "### Final Thoughts", "Calculating walkway area around a central pond is a straightforward yet essential geometric exercise. With just a few steps and the formula (A = 24\pi r^2), you gain a clear understanding of your circular space — perfect for informed design decisions in outdoor projects.", "---", "Keywords for SEO:\nCircular walkway area, pond walkway calculation, radius r walkway, area of circular ring, garden design math, walkway area formula, (5r) pond walkway, circle area subtraction, landscaping geometry", "Meta Description:\nDiscover how to calculate walkway area around a circular pond with outer radius (5r) minus the pond’s central circle. Step-by-step guide using the formula (A = 24\pi r^2) for accurate landscaping planning.", "---", "Optional Tagline:\nOptimize your outdoor space with precise circular area calculations — walk the path with confidence!"]
