The area of a circle is the measures of the space enclosed within its boundary. Here are all the main 3 methods through we can find area of the cricle.
Method 1: Using Radius (Most Common)
This is the most common & easy used method in which:
Formula: A = πr²
Where: A = Area
r = radius (distance from center to edge) π ≈ 3.14159
Example: Find the area of a circle with radius 5 cm.
A = π × 5²
A = π × 25
A = 78.54 cm²
Method 2: Using Diameter
In this method only diaeter has given we have to find radius first.
So, r = d / 2
Formula: A = π(d/2)² or A = πd²/4
Where d = diameter (distance across the circle through center)
Example: Find the area of a circle with diameter 10 cm.
A = π × (10/2)²
A = π × 5²
A = 78.54 cm²
OR:
A = π × 10² / 4
A = π × 100 / 4
A = 78.54 cm²
Method 3: Using Circumference
In this method only circumference has given we have to find radius first.
Where C = circumference (perimeter of the circle)
How it works: Since C = 2πr, we can solve for r and substitute into A = πr²
As C = 2πr – > r = C / 2π
r² = C / 2π -> r = C² / 4π
So Formula will be : A = C²/(4π)
Example: Find the area of a circle with circumference 31.42 cm.
A = 31.42² / (4π)
A = 987.42 / 12.566
A ≈ 78.54 cm²
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