Answer:
Explanation:
Since the circle is inscribed in the square, the diameter of the circle is equal to the side length of the square. Therefore, the diagonal of the square is twice the radius of the circle, or 10 mm.
To find the area of the square, we can use the formula A = s^2, where s is the side length of the square. The diagonal of the square is √2 times the side length, so we have:
10 mm = √2 x s
s = 10 mm / √2
The area of the square is:
A = s^2 = (10 mm / √2)^2 = 100 mm^2 / 2 = 50 mm^2
To find the area of the circle, we can use the formula A = πr^2, where r is the radius of the circle. We are given that the radius is 5 mm, so:
A = π(5 mm)^2 = 25π mm^2
To find the shaded section, we need to subtract the area of the circle from the area of the square. The shaded section is the remaining area of the square after the circle has been inscribed. Therefore, the shaded section is:
Shaded Section = Square Area - Circle Area
Shaded Section = 50 mm^2 - 25π mm^2
Shaded Section ≈ 10.79 mm^2 (rounded to two decimal places)