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how to derive the area of a circle. Area and circumference of a circle often gives our students their first taste of geometry during the year. This page looks to give a general run through of how the formula for the area of a circle can be derived.
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The equation of the circle shown above is given by x 2 y 2 a 2 The circle is symmetric with respect to the x and y axes hence we can find the area of one quarter of a circle and multiply by 4 in order to obtain the total area of the circle. One method of deriving this formula which originated with Archimedes involves viewing the circle as the limit of a sequence of regular polygons. In geometry the area enclosed by a circle of radius r is pr2.
First we draw a circle and its radius r.
Then draw another radius close to it so that it forms a small triangle-like figure. Usually they dont come to us understanding how to plug values into formulas. This page looks to give a general run through of how the formula for the area of a circle can be derived. It is reasonable then to replace 8s by 2 pi r which is the perimeter of the circle to calculate the area of the polygon or the circle when the number of sides is very big.
