A circle has a circumference of 31.4 units. What is its area? (Use \( \pi \approx 3.14 \))

["Circle with Circumference 31.4 Units: What Is Its Area?", "Understanding the relationship between a circle’s circumference and area is essential in geometry. In this article, we explore what a circle’s area is when its circumference measures exactly 31.4 units—using ( \pi \approx 3.14 )—and walk through the steps to calculate it.", "---", "### The Basics: Circumference and Radius", "The formula for the circumference ( C ) of a circle is:\n[ C = 2\pi r ]\nwhere ( r ) is the radius.", "Given that the circumference is 31.4 units, we substitute and solve for the radius:\n[\n31.4 = 2 \ imes 3.14 \ imes r\n]\n[\n31.4 = 6.28r\n]\n[\nr = \frac{31.4}{6.28} = 5 \ ext{ units}\n]", "So, the radius of the circle is 5 units.", "---", "### Calculating the Area from the Radius", "The formula for the area ( A ) of a circle is:\n[ A = \pi r^2 ]\nUsing ( \pi \approx 3.14 ) and ( r = 5 ):\n[\nA = 3.14 \ imes 5^2 = 3.14 \ imes 25 = 78.5 \ ext{ square units}\n]", "---", "### Final Result", "Therefore, a circle with a circumference of 31.4 units has an area of 78.5 square units.", "---", "### Why This Matters", "Knowing how to convert circumference to area helps in various real-world applications—from designing circular structures to solving engineering problems. This simple relationship demonstrates the elegance of geometric formulas and the power of using ( \pi ) in calculation.", "---", "Summary:\n- Circumference = 31.4 units\n- Radius = 5 units\n- Area ≈ 78.5 square units\n- Formula used: ( A = \pi r^2 ), ( \pi \approx 3.14 )", "Understanding these principles builds a strong foundation in mathematics and practical problem-solving."]