What is the Shaded Area?

[AglowOwl456]

Please could you explain how to get the answer. Thank you.

 

[pka]

You need to remove the sum of two circular segments from the area of the circle.
Draw the perpendicular bisector of \(\overline{AB}\) to see the two segments.

 

[MarkFL]

See if this diagram can help you get started:

 

[MarkFL]

To follow up:

I would compute the area \(A_S\) of the sector [MATH]ACD[/MATH]
[MATH]A_S=\frac{1}{2}(\sqrt{2})^2\frac{\pi}{4}=\frac{\pi}{4}[/MATH]
Now find the area \(A_T\) of the triangle [MATH]ACO[/MATH]
[MATH]A_T=\frac{1}{2}(1)(1)=\frac{1}{2}[/MATH]
Hence, the area \(A_1\) of [MATH]COD[/MATH] is

[MATH]A_1=A_S-A_T=\frac{\pi}{4}-\frac{1}{2}=\frac{\pi-2}{4}[/MATH]
Now, to find the shaded area \(A_2\), we subtract \(A_1\) from a quarter circle of radius 1:

[MATH]A_2=\frac{\pi}{4}-\frac{\pi-2}{4}=\frac{1}{2}[/MATH]
And then the total shaded area \(A\) asked for by the problem is 4 times \(A_2\):

[MATH]A=4A_2=2[/MATH]