Answer:
So first, we need to find the area of the whole circle since we already had the radius:
A = πr² = 3.14 . 7.53² = 178.040826 (cm²)
Now our next job is to find the area of the square inside the circle.
Looking at the picture, we can see that the radius of the circle is also half of the diagonal of the square, so the whole diagonal of the square should be: 7.53 . 2 = 15.06 (cm)
*Now this is where things get a little bit more complicated:
Imagine that x is the length of the side of the square.
Using Pythagorean theorem, knowing that d is the diagonal of the square and also the hypotenuse of the right triangle inside the square, we have the equation:
a² + a² = d²
2a² = d²
a² = d²/2
a² = 226.8036/2 = 113.4018
So a², which is also the area of the square, is 113.4018 (cm²)
So the are of the yellow region is: 178.040826 - 113.4018 ≈ 64.6 (cm²)
*I could be wrong though
