Answer: The area of the shaded portion is [tex](\pi-2)~\textup{sq. units}.[/tex]
Correct option is 2.
Step-by-step explanation: We are given to find the area of the shaded portion in the figure.
Since, the centre point of each arc is the corresponding central point of the line and the arcs intersect at the centre point of the circle,
so let us divide the figure into four equal parts, one of them is square ABCD as shown in the attached figure.
The area of the square ABCD will be
[tex]A_{ABCD}=\left(\dfrac{1}{2}\times 2\right)^2\\\\\\\Rightarrow A_{ABCD}=1~\textup{sq. units}.[/tex]
Now, area of the shaded portion inside the square ABCD will be
[tex]A_s=2\times \textup{area of the quarter circle with radius 1 unit}}-\textup{area of square ABCD}\\\\\Rightarrow A_s=2\times \left(\pi\times \left(\dfrac{1}{2}\right)^2\right)-A_{ABCD}\\\\\\\Rightarrow A_s=2\times\left(\dfrac{\pi}{4}\right)-1\\\\\\\Rightarrow A_s=\left(\dfrac{\pi}{2}-1\right)~\textup{sq. units}.[/tex]
Since all the four squares are identical in the attached figure, so the required area of the total shaded portion in the figure is
[tex]A=2\times\left(\dfrac{\pi}{2}\right)\\\\\\\Rightarrow A=(\pi-2)~\textup{sq. units}.[/tex]
Thus, the area of the shaded portion is [tex](\pi-2)~\textup{sq. units}.[/tex]
The correct option is 2.
