What is the formula for the area of a circle?

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What is the formula for the area of a circle?

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Answer 1 · 2017-03-03T17:45:01

$A = π \cdot r^{2} =$ $A=pi*r^2=$ area of a circle

Answer 2 · 2017-03-03T20:04:39

The formula $A = π r^{2}$ $A = pi r^2$ expresses the area of a circle in terms of its radius.

Explanation:

The number $π$ $pi$ is defined as the ratio of the circumference of a circle to its diameter (i.e. to twice its radius), hence the formula $2 π r$ $2 pi r$ .

The area of a circle is given by the formula:

$A = π r^{2}$ $A = pi r^2$

To see why, you can divide a circle into a number of equal segments and stack them head to tail to form a sort of parallelogram with 'bumpy' sides. The long sides will be about half the circumference in length - that is $π r$ $pi r$ , while the height of the parallelogram will be about $r$ $r$ . So the area is seen to be about $π r^{2}$ $pi r^2$ .

This approximation gets better the more segments you have, but here's an animated illustration I put together with just $8$ $8$ segments...

enter image source here

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What is the formula for the area of a circle?

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