# How do I find the shaded area?

This is how it looks like:

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?

• No, I mean the area between the smaller circle and larger circle, excluding all other shapes. – Wais Kamal Nov 17 '18 at 21:51
• 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. – achille hui Nov 17 '18 at 21:53

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 $$70\pi$$