Why am I not getting the correct answer?

[Guest]

Hello I am doing the following exercise.


Observe the following figure where [ABCD] is a square inscribed in a circle and circumscribed to another concentric circle with the first one.

Captura de ecrã_20230102_182133.png (81.7 KiB) Viewed 517 times

Knowing that the area of the larger circle is 100 and that the area of the square [ABCD] is 200 , determine the exact value
of the area of the colored region.
Displays the requested value in square meters.

Solution: (150pi-200)m^2

My Teacher hasn't lectioned geometry in detail only going into it to solve this types of problems so I'm kind of lost. But what I've done(with a lot of help online )is:

given
A1=100m^2
A2=200m^2

Colored Area = Area( smallcircle +Area(largecircle - square)
area of square is:
(a)^2=200
a=10sqrt(2)
We know that

a = diameter of small circle

Area of small circle = pi/4*d^2=pi/4*200=50pi
so the colored area is= 50pi+(100-200)m^2

I checked with a classmate and his answer was 257m^2
none of these match the answer in the book and I do not have the propper knowledge on how should i go about solving this exercise to percieve if any of these asnwers make sense .
Can You help me solve this
Your time and attention are deeply appreciated
Thank You.

[Guest]

Did you manage to solve it?
You have to find the radius (diameter) of the small circle.
Then the answer is: 100 - the area of the square + the area of the small circle
The square side is equat to the small circle diameter.