Theory:

The perimeter of the sector:
The perimeter of the sector is defined as the sum of the two radii OA(r), OB(r) and the length of the arc AB(l). It looks like a piece of a pie or a piece of pizza.
 
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Perimeter \(= r+r+l=2r+l\) units.
The perimeter of a semicircle:
The perimeter of a semicircle is defined as the sum of the two radii OA(r), OB(r) and the length of the arc AB(l). In this, we substitute the value of \(l =\) πr.
 
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Perimeter of a semicircle = \(l+2r\) (where \(l=\pi r\)).
 
\(=\pi r + 2 r = (\pi + 2)r\) units.
The perimeter of a circular quadrant:
The perimeter of a circular quadrant is defined as the sum of the two radii OA(r), OB(r) and the length of the arc AB(l). In this, we substitute the value of \(l =\) πr2.
 
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Perimeter of a quadrant = \(l+2r\) (where \(l=\frac{\pi r}{2}\)).
 
\(=\frac{\pi r}{2} + 2r = \left(\frac{\pi}{2} + 2 \right) r\) units.