A circle is inscribed in a square with side length 10 cm. Find the area of the circle.
["Title: How to Find the Area of a Circle Inscribed in a Square – Step-by-Step Guide", "When a circle is inscribed in a square, the circle fits perfectly inside the square, touching all four sides. This relationship gives strong geometric clues that help solve related area problems. In this article, we explore a classic example: a square with side length 10 cm, in which a circle is perfectly inscribed. We’ll walk through how to determine the area of that circle step by step.", "### What Does It Mean for a Circle to Be Inscribed in a Square?", "A circle inscribed in a square has a diameter equal to the side length of the square. Because the circle touches each side of the square exactly once, its diameter matches the square’s edge. This simple relationship makes calculating the circle’s area straightforward.", "### Step 1: Identify the Square’s Side Length", "We are given that the square has a side length of:\n10 cm", "### Step 2: Determine the Diameter of the Inscribed Circle", "Since the diameter of the circle equals the side length of the square:\nDiameter = 10 cm", "### Step 3: Calculate the Radius of the Circle", "The radius is half of the diameter. So:\nRadius = Diameter / 2 = 10 cm / 2 = 5 cm", "### Step 4: Use the Area Formula for a Circle", "The area ( A ) of a circle is calculated using the formula:\n[\nA = \pi r^2\n]\nwhere ( r ) is the radius.", "Substituting ( r = 5 ) cm:\n[\nA = \pi (5)^2 = \pi \ imes 25 = 25\pi , \ ext{cm}^2\n]", "### Final Answer", "The area of the circle inscribed in a square with a side length of 10 cm is:\n( 25\pi , \ ext{cm}^2 )\n(approximately 78.54 cm² when using ( \pi \approx 3.1416 ))", "---", "### Why Understanding This Matters", "Knowing how to find the area of an inscribed circle helps in real-world applications such as design, architecture, engineering, and geometry problem-solving. This fundamental relationship between squares and their inscribed circles lays the foundation for more advanced geometry topics like trigonometry and calculus.", "Key Takeaway: Always remember that the diameter of an inscribed circle in a square equals the square’s side length—this simple insight simplifies area calculations dramatically.", "---", "Keywords: circle inscribed in square area, area of inscribed circle, geometry problems, square diameter circle radius, circle area formula, inscribed circle geometry, 10 cm square area calculation\nMeta Description: Learn how to find the area of a circle inscribed in a 10 cm square using simple geometry. Step-by-step solution with radius, diameter, and formula application."]
