A circle is inscribed in a square. If the side of the square is 14 cm, find the area of the circle. Use \( \pi \approx 3.14 \).
["Circle Inscribed in a Square: Find the Area When Side of Square is 14 cm", "When it comes to geometric shapes, one classic relationship involves a circle perfectly fitting inside a square — known as a circle inscribed in a square. Understanding this configuration not only helps in geometry problem-solving but also lays the foundation for real-world applications in design, architecture, and manufacturing.", "In this article, we’ll explore how to determine the area of an inscribed circle when the side of the square is given. Let’s break it down step by step using a practical example where the square’s side measures 14 cm.", "### What Does It Mean for a Circle to Be Inscribed in a Square?", "If a circle is inscribed in a square, it means the circle touches all four sides of the square from the inside — it fits snugly. The diameter of the circle is exactly equal to the side length of the square, and its radius is half that length.", "### Given Information", "- Side length of the square = 14 cm\n- Since the circle touches all four sides:\nDiameter of the circle = 14 cm\nRadius of the circle = Diameter ÷ 2 = 14 ÷ 2 = 7 cm", "### Formula for the Area of a Circle", "The area of a circle is calculated using the formula:\n[\n\ ext{Area} = \pi r^2\n]\nwhere ( r ) is the radius and ( \pi \approx 3.14 ) for approximate calculations.", "### Step-by-Step Calculation", "1. Substitute radius ( r = 7 ) cm and ( \pi \approx 3.14 ):\n[\n\ ext{Area} = 3.14 \ imes (7)^2\n]\n2. Compute ( 7^2 = 49 ):\n[\n\ ext{Area} = 3.14 \ imes 49\n]\n3. Multiply:\n[\n\ ext{Area} = 153.86 \ ext{ cm}^2\n]", "### Final Answer", "Thus, the area of the inscribed circle is approximately 153.86 cm².", "### Why This Relationship Matters", "This geometric principle is not just theoretical. Designers use such relationships to optimize space, engineers rely on accurate area calculations for material estimation, and educators use these concepts to build logical reasoning in students.", "Bottom line:\n- Side of square = 14 cm\n- Radius of inscribed circle = 7 cm\n- Area of circle = 153.86 cm²", "Next time you see a square with a perfectly fitting circle inside, remember: geometry makes practical sense — and math like this brings clarity to design and space planning!", "---\nKeywords: inscribed circle in square, area of circle formula, side of square 14 cm, geometry demo, circle and square relationship, area calculation with π, math problem solved"]
