Suppose you are given a square with an inscribed circle if the area of the square is 100 meters squared what is the area of the circle?



Diameter of the circle is also the length of a side of the square, $10$ units.

  • $\begingroup$ Would I do pir^2 with radious of five? $\endgroup$ – El Cholo Grande Apr 23 '12 at 14:08
  • $\begingroup$ Exactly. BTW, this site allows you to use TeX mark up for the Math. So, you'd write the area of the circle $\pi r^2$ as $\pi r^2$. Regards, $\endgroup$ – user21436 Apr 23 '12 at 14:09

Note that area of a square is given by $s^2$ where $s$ is the length of one of its sides (whichever side it may be, it doesn't matter for they are all equal.

So if $s^2=100 \implies s=\sqrt{100}=10 \text{ meters}$. The side of your square is $ 10$ meters. A circle inscribed in it would look something like this


Now Note that in the diagram, Since $\bar{DC}=10\text{ meters} \implies \bar{XY}= \bar{DC}=10 \text{m}$.

So we now have that the diameter $XY$ of the circle at $O$ is $10\text{ meters}$.(I made a mistake while making the diagram, it should have been $10 \text{m}$ not $10 \text{cm}$, I hope this won't be much of a problem)
Figuring out the area of a circle with a given diameter is an elementary geometry problem. The area of the circle hence is $\pi\cdot\big(\frac12\cdot10\text{m}\big)^2=(25\pi)\;\text m^2$

  • 1
    $\begingroup$ I gave this answer a +1 for filling in what my post lacked. $\endgroup$ – user21436 Apr 24 '12 at 7:12
  • $\begingroup$ @KannappanSampath ahaha, thanks mate :) $\endgroup$ – funktor Apr 24 '12 at 11:28

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