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This is how it looks like:

enter image description here

It is given that the area of the shaded region is $35 cm^2$.

All of my attempts so far ended up in a two-variable equation in terms of $r_1$ and $r_2$ (the radii of the larger circle and smaller circle respectively).

So, how do I find the area enclosed between the two circles, that is, the area of the larger circle minus the area of the smaller circle?

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  • $\begingroup$ No, I mean the area between the smaller circle and larger circle, excluding all other shapes. $\endgroup$ – Wais Kamal Nov 17 '18 at 21:51
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    $\begingroup$ Then the hint becomes $\frac12(r_1^2-r_2^2) = 35 \implies \pi(r_1^2-r_2^2) = ?$ which is essentially what Manika's answer does. $\endgroup$ – achille hui Nov 17 '18 at 21:53
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Say $R_s$ is the radius of small circle and $R_b$ is the radius of big one, then

  1. What you need to find is $S = \pi*(R_{b}^2 - R_{s}^2)$
  2. What you already know is $0.5R_b^2 - 0.5R_s^2 = 0.5(R_b^2 - R_s^2) = 35$ (subtracting the areas of triangles)

From (2) you just find, that $R_b^2 - R_s^2 = 70$ and then substituting it into (1) you get $70\pi$

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  • $\begingroup$ Never thought it is that simple, thanks a lot dude :) $\endgroup$ – Wais Kamal Nov 17 '18 at 21:54

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