The perimeter is \(4s = 4 \times 5\sqrt{2} = 20\sqrt{2}\) cm.
["# Perimeter of a Square: How to Calculate (4s = 4 \ imes 5\sqrt{2} = 20\sqrt{2}) cm", "Calculating the perimeter of a square is a fundamental geometry task that is both simple and essential for understanding shapes in math, architecture, design, and everyday measurements. In this article, we will explain how to find the perimeter using the given side length (s = 5\sqrt{2}) cm, arriving at the precise result:\n[ 4s = 4 \ imes 5\sqrt{2} = 20\sqrt{2} \ ext{ cm} ]", "---", "## What Is the Perimeter of a Square?", "The perimeter of a polygon is the total distance around its boundary. For a square — a four-sided shape with all sides equal in length — the perimeter is calculated using the formula:", "[\n\ ext{Perimeter} = 4s\n]\nwhere (s) is the length of one side.", "---", "## Applying the Formula with (s = 5\sqrt{2}) cm", "Given that each side of the square is (s = 5\sqrt{2}) cm, we multiply this length by 4 to find the total perimeter:", "[\n\ ext{Perimeter} = 4s = 4 \ imes 5\sqrt{2}\n]", "Step-by-step:\n[\n4 \ imes 5 = 20\n]\n[\n\Rightarrow \ ext{Perimeter} = 20\sqrt{2} \ ext{ cm}\n]", "---", "## Understanding the Calculation", "- (5\sqrt{2}) cm represents a diagonal-adjusted side length, possibly derived from a geometric figure like a square inscribed in a circle or a coordinate geometry setup.\n- Multiplying by 4 gives the total distance around the square — a key measure in construction, carpentry, and range estimation.\n- Using (\sqrt{2}) emphasizes irrational, non-integer dimensions, important in advanced math and real-world applications like diagonal distance conversions.", "---", "## Why Is This Perimeter Significant?", "- Precision in Measurement: Knowing exact values ensures accuracy in building, landscaping, or crafting.\n- Mathematical Foundation: Reinforces understanding of polygons and algebraic expressions.\n- Real-Life Applications: Useful for tiling floors, fencing yards, or designing rectangular/square layouts.", "---", "## Summary", "Calculating the perimeter of a square is straightforward: multiply the side length by 4. For a side of (5\sqrt{2}) cm, this yields a clean, exact result of\n[ 4s = 4 \ imes 5\sqrt{2} = 20\sqrt{2} \ ext{ cm} ]\nThis expression not only reflects the geometric properties of the square but also supports precise, real-world applications.", "---", "Keywords: perimeter of a square, calculate perimeter, side length (5\sqrt{2}) cm, geometry formula, square perimeter formula, (4s = 20\sqrt{2}), exact measurement.", "Back to all geometry guides — mastering perimeters starts here!"]
