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    Area of circle and stuff I am sooo confused about. Not really in any of the courses I've taken, but I've seen it and I'm confused.

  • MOD

    Hi @The-Darkin-Blade!
    Nice to hear from you again!
    The area of circle is a veeery big topic for a small forum post. There are lots of articles about the formula of a circle's area and other things related to this topic! Hundreds! Even thousands!
    Your confusion is normal 🙂
    To learn more about it, you can start from here, or find more advanced information here.

    You can also imagine that a circle is a regular polygon with lots and lots of vertices (actually, infinitely many vertices). To find the area of a regular polygon, you cut it into isosceles triangles (see picture) and then sum up their areas. So the area of a polygon is equal to \(n\times(\frac{1}{2}ah)=\frac{h}{2}\times(na),\) where \(n\) - number of vertices, \(a\) - side length and \(h\) - distance from the center of polygon to its side. The term \(na\) is the perimeter of the polygon. As the polygon becomes more and more like a circle, this value approaches the value of the circle's circumference, which is \(2\pi r,\) and value of \(h\) approaches the circle radius. So, substituting \(2\pi r\) instead of \(na,\) we get: \(\text{area of circle}=\frac{r}{2}\times(2\pi r)=\pi r^2.\)

    Studying this in more detail and discovering lots of new and very interesting things will be easier as you get older and study higher-level topics like functions, derivatives, integrals, and many other things. 😉