The circle

Define the side $a$ of a square of apexes $ABCD$.
Two arcs $P$ and $Q$ are drawn centered, respectively, in $B$ and $D$. Both measure $90^\circ$, start in $A$ and end in $C$. Find the length of the arcs $P$ and $Q$.
Determine the area inside the square and out of the diagram that is bounded by the arcs $P$ and $Q$.

We define the side of the square as $a=10$.
Both are arcs of $90^\circ$ of circumferences, of radius $10$. And so, they will have a length of the quarter of the perimeter of the circumference of radius $10$: $$l_p=l_q=\dfrac{2\pi\cdot r}{4}$$ $$l_p=l_q=5\pi$$
We first find the area of one of the two areas that are inside the square and out of the diagram formed by the arcs $p$ and $q$. This area will take as an area the difference between the area of the square and the area of a sector of $90^\circ$ of the circle of radius $10$.

$$\mbox{Area} \ ACD = \mbox{Area} \ ABCD - \mbox{Area sector} \ BCA$$ $$A_{ACD}=100-\dfrac{\pi \cdot 10^2}{4}=21,4$$ $$A_{total}=A_{ACD}+A_{ACB}=2\cdot A_{ACD}=42,8$$

$a=10$
$l_p=l_q=5\pi$
$A_{BLUE}=42,8$

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