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Suppose the radius of the circle is r units.

Then perimeter of a whole circle = 2*pi*r.

So perimeter of curved part (arc) of a quarter circle = 2*pi*r / 4 = pi*r/2

Also, the quadrant has a radius on either end of the curved part. Their combined length is 2*r

So the total perimeter = 2r + pi*r/2 = r(2 + pi/4)

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Q: What is the formula of the perimeter in the quarter of the circle?
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