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how to find area of circle

The area of a circle is found with the formula
Area=πr2\text{Area}=\pi r^2Area=πr2, where rrr is the radius of the circle.

Quick Scoop

1. Core idea

  • A circle’s area is how much flat space it covers inside its boundary.
  • The key ingredient is the radius : the distance from the center of the circle to any point on the edge.
  • Once you know the radius, you square it (multiply it by itself) and then multiply by π\pi π (about 3.14).

So the main formula is:

Area=πr2(π≈3.14)\text{Area}=\pi r^2\quad (\pi \approx 3.14)Area=πr2(π≈3.14)

2. Step‑by‑step: using the radius

  1. Find the radius
    • If you already have the radius, use it directly.
    • If you’re given the diameter instead, divide it by 2 to get the radius.
  1. Square the radius
    • Compute r2=r×rr^2=r\times rr2=r×r.
  1. Multiply by π\pi π
    • Area = π×r2\pi \times r^2π×r2.

Example: radius r=3r=3r=3 cm

  • r2=3×3=9r^2=3\times 3=9r2=3×3=9
  • Area ≈3.14×9=28.26\approx 3.14\times 9=28.26≈3.14×9=28.26 cm²

3. If you know the diameter

Sometimes you’re given the diameter ddd (the distance all the way across the circle through the center).

  • Relationship: d=2r⇒r=d2d=2r\Rightarrow r=\dfrac{d}{2}d=2r⇒r=2d​.
  • Plugging that into the area formula gives another useful version:

Area=πd24\text{Area}=\frac{\pi d^2}{4}Area=4πd2​

So you can either:

  • First find the radius r=d/2r=d/2r=d/2, then use πr2\pi r^2πr2, or
  • Directly use Area=(π/4) d2\text{Area}=(\pi/4),d^2Area=(π/4)d2.

4. If you know the circumference (edge length)

If you are told the circumference CCC (the length around the circle), you can still find the area.

You have:

  • C=2πr⇒r=C2πC=2\pi r\Rightarrow r=\dfrac{C}{2\pi}C=2πr⇒r=2πC​.

Substitute into the area formula:

Area=πr2=π(C2π)2=C24π\text{Area}=\pi r^2=\pi \left(\frac{C}{2\pi}\right)^2=\frac{C^2}{4\pi}Area=πr2=π(2πC​)2=4πC2​

So another formula is:

Area=C24π\text{Area}=\frac{C^2}{4\pi}Area=4πC2​

5. Tiny story to remember it

Imagine slicing a circle into many thin “pizza slices” and rearranging them into a shape that looks more and more like a rectangle.

  • One side of that rectangle is about half the circumference: πr\pi rπr.
  • The other side is the radius rrr.
  • Rectangle area = length × width = πr×r=πr2\pi r\times r=\pi r^2πr×r=πr2.

That rearranged-pizza picture is a mental shortcut for why the area formula πr2\pi r^2πr2 makes sense. TL;DR:

  • Main formula: Area=πr2\text{Area}=\pi r^2Area=πr2.
  • With diameter ddd: Area=πd24\text{Area}=\dfrac{\pi d^2}{4}Area=4πd2​.
  • With circumference CCC: Area=C24π\text{Area}=\dfrac{C^2}{4\pi}Area=4πC2​.

Information gathered from public forums or data available on the internet and portrayed here.