Area of Circle

📐 Area of a Circle – Complete Guide with Formula, Examples & Calculator

The Area of a Circle is one of the most important topics in basic geometry and is frequently asked in Class 9 and Class 10 Mathematics exams. Understanding how to calculate the area of a circle not only helps in board exams but is also useful in real-life applications like construction, design, and engineering. In this article, you will learn the definition, formula, examples, and practical uses of the area of a circle in a simple and clear way.

---

🔵 What is a Circle?

A circle is a round-shaped figure in which all points on the boundary are at the same distance from a fixed point called the center.
The distance from the center to the boundary of the circle is called the radius (r).

---

📏 What is the Area of a Circle?

The area of a circle is the amount of space enclosed within its boundary. It is always measured in square units, such as square centimeters (cm²), square meters (m²), etc.

---

🧮 Formula for Area of a Circle

The standard formula to calculate the area of a circle is:$$\text{Area of Circle} = \pi r^2$$Area of Circle=πr2

Where:

• π (pi) ≈ 3.14
• r = radius of the circle

---

✏️ Examples of Area of a Circle

Example 1:
Find the area of a circle with radius 7 cm.$$\text{Area} = \pi r^2 = 3.14 × 7 × 7 = 153.86 \text{ cm}^2$$Example 2:
If the radius of a circular park is 14 m, find its area.$$\text{Area} = 3.14 × 14 × 14 = 615.44 \text{ m}^2$$Area=3.14×14×14=615.44 m2

These types of questions are very common in school exams.

---

🔄 Area of Circle Using Diameter

Sometimes, the diameter (d) is given instead of the radius.
Since radius = diameter ÷ 2, the formula becomes:$$\text{Area} = \pi \left(\frac{d}{2}\right)^2$$Area=π(2d​)2