Question

I don’t understand how to do this?

Answer 1

To solve you need to first find the area of the shaded region and the non shaded region:
non shaded region:Remember the formula for the area of a circle is π.r^2.To find the radius of the small circle look at the square.The square's width is equal to the small circle's diameter.That means the radius is 10/2 which is 5.plug it into the equation and you get π(5)^2 which is 25πThe small circle's area is therefore 25π
Now let us find the area of the shaded region.We do this by finding the area of the big circle and subtract the area of the small circle from it.
Finding the radius of the big circle is a bit more tricky. We need to solve for the hypotenuse of the square.
To make it easier, I'm gonna use the 45-45-90 special triangle method.You can look it up later, but essentially I can figure out that the hypotenuse of square is 10√2.The radius is half of that so; 5√2
Plug it into the equation and you get π(5√2)^2 which is 50π
Now we need to subtract area of small circle from area of big circle. 50π-25π = 25π

That means the shaded portion is 25π.
The area of the small circle is also 25π so both areas equal each other.