geometry

Let's first find the outer shaded region, not the one in the square.

Square is 1cm

Two quarter circles equal pi/2 cm

The big quarter circle is pi cm

So the outer area is pi/2-1 cm

The inner part in the square is a 90 degree sector of a circle with radius 1 minus an isosceles right triangle with side 1 (two of them in total).

pi/4-1/2 times 2 equals pi/2-1

Add them up to get

\(\pi -2\) cm^2.

You are very welcome!

:P

The area  of (1/2)  the shaded  region inside the square is  =

Area of a quarter circle with a radius of 1cm  -  area of a right triangle with legs  of 1 cm  =

 pi (1)^2/ 4 -  (1/2)(1)^2  =

( 1/2)  [ pi/2 - 1]

So...usihg symmetry this shaded area  =    [ pi/2 - 1]

And the outer shaded area =

Area of a quarter circle with  a radius   of 2 cm   -  area of two quarter circes  with a radius  of 1 cm  - square with a side of 1 cm    =

pi * (2)^2 / 4  -   2* pi (1)^2 / 4  -  1  =

pi  -  (1/2)pi  -  1  =

(pi/2)- 1

So....the toal shaded area  =  

2 [ pi/2 - 1 ] =

(pi  - 2)   cm^2

Find the area of the shaded region.

The area of the shaded region    A_s = π - [ π/2 + 1 - 2( π/4 - 1/2 )]