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

["Understanding Circle Geometry: Finding Area When Circumference is Known", "Are you curious about how to calculate the area of a circle when given its circumference? In this article, we’ll explore a practical example to help you master this fundamental skill in geometry—perfect for students, teachers, and math enthusiasts alike.", "---", "### Given:\nA circle has a circumference of 31.4 meters, and we’ll use ( \pi \approx 3.14 ) for calculations.", "---", "### Step 1: Recall the Formula for Circumference\nThe formula for the circumference ( C ) of a circle is:\n[\nC = 2\pi r\n]\nwhere ( r ) is the radius.", "---", "### Step 2: Solve for the Radius\nUsing the given circumference:\n[\n31.4 = 2 \ imes 3.14 \ imes r\n]\n[\n31.4 = 6.28 \ imes r\n]\nTo find ( r ), divide both sides by 6.28:\n[\nr = \frac{31.4}{6.28} = 5 \ ext{ meters}\n]", "---", "### Step 3: Use the Radius to Find the Area\nThe formula for the area ( A ) of a circle is:\n[\nA = \pi r^2\n]\nSubstitute ( r = 5 ) meters and ( \pi \approx 3.14 ):\n[\nA = 3.14 \ imes (5)^2 = 3.14 \ imes 25 = 78.5 \ ext{ square meters}\n]", "---", "### Final Answer:\nThe area of the circle is 78.5 square meters.", "---", "### Why This Matters\nKnowing how to derive area from circumference reinforces your understanding of key circle properties and can help in real-world applications such as engineering, architecture, and design. Whether planning a garden bed, a circular plot, or calculating material needs for circular structures, mastering these formulas saves time and prevents errors.", "---", "Key Takeaways:\n- Circumference ( C = 2\pi r ) detects radius\n- Area ( A = \pi r^2 ) builds on radius to find area\n- Using ( \pi \approx 3.14 ) provides fast, practical approximations", "Whether you're solving textbook problems or tackling practical challenges, understanding this relationship makes geometry more intuitive and applicable.", "If you found this guide useful, share it with fellow learners—and keep practicing your circle calculations!", "---", "Math made simple. Geometry within reach."]