A circle is inscribed in a square with a side length of 14 cm. Calculate the area of the circle. Use \( \pi \approx 3.14 \).
["A Circle Inscribed in a Square: Calculating the Area of the Inscribed Circle", "When a circle is inscribed inside a square, the diameter of the circle equals the side length of the square. In this article, we explore the geometry behind this classic configuration, specifically when the square has a side length of 14 cm. We’ll also calculate the area of the circle using ( \pi \approx 3.14 ).", "---", "### Understanding the Geometry: Circle Inscribed in a Square", "A square has four equal sides and four right angles. When a circle is inscribed in a square, it touches all four sides exactly at their midpoints. This means the diameter of the circle is equal to the length of one side of the square.", "Given:\nSquare side length = 14 cm\nTherefore, diameter of the circle = 14 cm\nAnd thus, the radius ( r ) is half of the diameter:\n[\nr = \frac{14}{2} = 7 \ ext{ cm}\n]", "---", "### Calculating the Area of the Inscribed Circle", "The formula for the area ( A ) of a circle is:\n[\nA = \pi r^2\n]", "Using ( \pi \approx 3.14 ) and ( r = 7 ) cm:\n[\nA \approx 3.14 \ imes (7)^2 = 3.14 \ imes 49 = 153.86 \ ext{ cm}^2\n]", "So, the area of the inscribed circle is approximately 153.86 cm².", "---", "### Summary", "In a square with side length 14 cm, the inscribed circle perfectly fits within, with a diameter matching the square’s side. The area calculation becomes simple and straightforward once the radius is determined. This relationship between squares and inscribed circles is fundamental in geometry and widely applicable in design, engineering, and mathematics.", "---", "Try It Yourself:\nNext time you encounter a square with an inscribed circle, remember: diameter = side length → radius = half the side → area = ( \pi r^2 ). For 14 cm, it’s about 153.86 cm² — a neat and practical application of geometry!", "---", "Keywords: inscribed circle, square, circle area, geometry, ( \pi ), side length 14 cm, radius calculation"]
