First find the area of the circle.
area = πr²
area = π(5²) = (25π) cm²
Then find the area of the square. To find that, construct a right triangle where the length indicated is the hypotenuse. Then use the pyth. theorem.
a²+b²=c²
Because the other two legs of the triangle are equal...
a²+a²=c²
2a²=c²
2a²=5
a²=2.5
a=(√2.5) cm²
Now we need to find the side length of the square which is twice the length of the legs in the triangle.
side length = 2√2.5 = (√10) cm²
And then we can find the area of the square.
area = √10 × √10 = 10 cm²
Lastly we subtract the area of the square from the area of the circle to get the area of the shaded region.
area = 25π-10 = 68.54 cm² approx.