I am stuck at calculating the surface area for this shape (only red area). I know how to calculate some area, but not sure how to substract area
$$P = \frac{20 \cdot 10}2 = 100 - 25\pi\, -\, ?$$
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2I suspect that's the highschool chaining notation; give a kid $12+5+23$ and he'll do $12+5=17+23=40$, meaning, $[12+5=17][17+23=40]$ – Oct 12 '17 at 11:56
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1You want the red area or the area marked by the red arrow? – SchrodingersCat Oct 12 '17 at 11:57
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I want the red area – safety Oct 12 '17 at 12:03
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I need to get surface of area marked only in red. As I said, I don't know how to substract area marked by the red arrow. Or there is another way to get surface? – safety Oct 12 '17 at 12:29
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Segment $x$ is twice $y$ because the rectangle base is twice the height.
The second equation is Pythagora's Theorem
$ \left\{ \begin{array}{l} x=2 y \\ (5-x)^2+(5-y)^2=25 \\ \end{array} \right. $
we get $(5-2y)^2+(5-y)^2=25$
$y^2-6 y+5=0 \to y_1=1;\;y_2=5$
$x=2;\;y=5$ is the point where diagonal and circle intersect
So we have $\sin\alpha=\frac{3}{5}$
The area $\mathcal{S}$ we are calculating is composed by the green triangle and the pink curved part. The pink part is the trapezoid less the sector with angle $\alpha$
$$\mathcal{S}=\frac{2\times 1}{2}+\left(\frac{3\times(1+5)}{2}-\frac{25 \pi }{\arcsin\left(\frac{3}{5}\right)}\right)\approx 1.95624$$
Hope this is useful
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Raffaele
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