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a region is bounded by semicircular arcs constructed on the side of a square whose sides measure $2/\pi$, as shown. what is the perimeter of this region?

Sagot :

According to the question, a region is bounded by semicircular arcs on the side of the squares. Therefore, the side of the square is the diameter of the circle.

And the side of the square is [tex]\frac{2}{\pi }[/tex].

Now, the radius of the semicircle is [tex]\frac{1}{2} \frac{2}{\pi } =\frac{1}{\pi }[/tex]

The length of the semicircular arc is equal to half the circumference of the corresponding circle.

Therefore, the length of the arc is [tex]\frac{1}{2} (2)(\pi)\frac{1}{\pi } =1[/tex]

Now, the desired parameters of the region made by these arcs is [tex](4)(1)=4[/tex]

What are semicircular arcs and circumference of the circle?

Semicircular arcs is another name for the semicircle. It divides the circle into two parts. And the endpoints on a circle defines the minor arc or major arc. Similarly, circumference is the perimeter of the circle.

To learn more about the semicircular arcs and circumference of the circle from the given link:

https://brainly.com/question/17329757

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