Answer:
To find the area of the shaded region, we first need to determine the area of the square and the area of the circle. Then, we can subtract the area of the circle from the area of the square to obtain the shaded region.
The area of a square is calculated by multiplying the length of one side by itself. In this case, since the side length of the square is given as 18mm, we can calculate its area as follows:
Area of square = (side length)^2
Area of square = 18mm * 18mm
Area of square = 324mm^2
Next, let's calculate the area of the circle. The area of a circle is given by the formula:
Area of circle = π * (radius)^2
Since we are given the side length of the square, we can use it to find the diameter and radius of the circle. The diameter is equal to the side length of the square, and the radius is half of the diameter. Therefore:
Diameter = 18mm
Radius = Diameter / 2
Radius = 18mm / 2
Radius = 9mm
Now we can calculate the area of the circle using this radius:
Area of circle = π * (9mm)^2
Area of circle ≈ 254.47mm^2
Finally, to find the area of the shaded region, we subtract the area of the circle from the area of the square:
Shaded region = Area of square - Area of circle
Shaded region = 324mm^2 - 254.47mm^2
Shaded region ≈ 69.53mm^2
Therefore, the area of the shaded region is approximately 69.53 square millimeters.
Explanation: