The area of the shaded region is = (72π - 144) mm²
What is the area of a shaded region?
The area of a shaded region is that enclosed part of a plane figure that is shaded.
Suppose;
- A square is inscribed in a circle with a diameter of 12√2 millimeters.
- Everything outside of the square is shaded.
Let's first find the area of the circle.
Area of circle = [tex]\mathbf{\pi r^2}[/tex]
Area of circle = [tex]\mathbf{\pi \times (\dfrac{12 \sqrt{2}}{2})^2}[/tex]
Area of circle = 72π sq mm
We know that the side of the inscribed square = [tex]\mathbf{\dfrac{12\sqrt{2}}{\sqrt{2}}}[/tex] = 12 mm
Area of the square = side(L)²
Area of the square = 12²
Area of the square = 144 sq mm
Now, the area of the shaded region can be estimated by finding the difference between the area of the square from that of the circle.
i.e.
The area of the shaded region is = (72π - 144) mm²
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