Is it possible to draw a circle when we know its area?

This question doesn't provide enough information to say. Do you mean draw it physically?  Or represent it mathematically?  Are we expected to know the position of the circle, or can it be represented arbitrarily?  You say we "know its area", but do we know it numerically, or do we know it in relation to some other thing that we might not know? You claim that there's a more difficult problem that this is related to-- and this is such a trivial question that we're left wondering what the catch is (seems like a troll post in some ways). Drawing things both physically and perfectly is impossible.  You can't even draw a perfect 2" line physically.  The real world is way too sloppy.  But you can draw things that are "close enough" for certain purposes.  And chances are we can do that no problem. The other component is if the exact position also needs to be derived.  If you know 3 distinct points on the edge of the circle, you're good.  If you only know 2 distinct points, then there's 2 possible circles to draw.  If you only know 1 distinct point on the edge, then there's an infinite number of circles you could draw.  You might also know points contained within the circle, or the center of the circle, or some set of lines that are tangent to the circle, etc.  But we'd have to know more.

yes, it is possible by comparing area with [(pi)(square of radius)] and finding out the radius. After that, draw a circle of the radius calculated.

I believe the answer is "Yes." The question really boils down to "Can we draw a line whose length is an irrational number?" Obviously, we know that A = pi*r^2, and can calculate that r = sqrt(A/pi). However, it is possible (likely, in fact) that this r is an irrational number, so the question is "Can we draw a circle whose radius is an irrational number" or more simply, "Can we draw a line whose length is an irrational number?" I believe the answer to this question is "Yes." Assume we have one point at (0,0) of our coordinate system. The question is, is it possible to have a point at ( x, 0) where x is an irrational number? Since space is continuous (i.e. you can go infinitely small), then there does exist a location within space that is a distance x away from (0,0). Another way to look at it is to bound the solution. Can you draw a circle that has a larger area? Yes. Can you draw a circle that has a smaller area? Yes. So the circle containing your area must lie somewhere in the continuous space between those two solutions. So certainly there is a circle containing that area. If you're asking whether it's possible for us to draw that EXACT circle intentionally, that's more of a question of our capabilities as human beings. However, because the circle exists, I would argue that the possibility to draw it also exists, infinitesimally small though it may be. Think about it another way: Let's say I draw a random circle. That random circle has an area of (for example) A. What makes A any more or less precise than the area you're asking for? Had you asked me to draw a circle of area A, I would have already done so. Drawing the circle is possible. Drawing it on command is up for question. However, I add the disclaimer that I am not a mathematician or math major. It's certainly an interesting question that I think delves deep into the basic assumptions/axioms behind our mathematical system (particularly continuous math).

"Squaring the circle, " which is equivalent to your problem, is impossible. http://en.wikipedia.org/wiki/Squaring_the_circle In mathematics, there is a big difference between equal and approx. equal, especially when proofs of famous math problems are concerned.

I don't know which famous problem is related to this but if you know the area of a circle, you know it's radius. If you know the radius of a circle, you can draw it using a compass etc. The area does not contain the center information so the drawn circle's center can be anywhere. Now, what is this famous problem about and how is it related to this ?

Is this question about math? Or is it about the drawing ability of human? If it is a math question, then you need to clarify what you mean by "draw". Do you mean http://en.wikipedia.org/wiki/Compass-and-straightedge_construction (in this case it is impossible due to http://en.wikipedia.org/wiki/Squaring_the_circle)? What instruments are allowed (and what can they do in the idealized setting of geometrical construction)? The word "draw" has no meaning in math unless you clearly define what it is. Without defining it, the question "Is it possible to draw ..." is meaningless. It just doesn't make sense in math. If this is a question about drawing ability, then I don't really know. Of course no one can draw mathematically perfect circles with exactly the given area, so you have to tolerate some imprecision. I myself can draw circles freehand pretty well, though I am not sure if I can draw a circle freehand with area 10cm^2 (perhaps a tolerance of +/- 1cm^2) in one shot. But a question about drawing ability is probably unrelated to your "one of the most famous Math problem". (Does what I said about my drawing ability sounds like anything to do with math?) Math works in an idealized world. You can't prove a math theorem by saying something like "I have drawn a circle with area 1 on this paper, so squaring the circle must be possible". And frankly, though I don't know which famous math problem you are referring, the chance that the answer to this question can be used to solve a well-known unsolved math problem is very slim.

: Hey hey hey...that is not the idea. You cannot do the math. That is the whole point of constructing. Otherwise squaring the circle is cheesecake. (Anyway you're not given a ruled straight-edge) This is not a solution but more of an intuition. Say the area of A units. Cut a yarn of length, A units and roll it into a circle. There you have it! Of course this isn't a solution.

Definitely. You just need to calculate the radius of the circle using formula \pi r^2 = Area r = \sqrt{Area/\pi} And to draw a circle all you need is the radius. Good luck!!!!