15. Perimeter of sector, semicircle and quadrant circle

The perimeter of the sector is defined as the sum of the two radii $\mathit{OA}(r)$, $\mathit{OB}(r)$ and the length of the arc $\stackrel{⌢}{\mathit{AB}}(l)$. It looks like a piece of a pie or a piece of pizza.

 

 

Perimeter \(= r+r+l=2r+l\) units.

The perimeter of a semicircle is defined as the sum of the two radii $\mathit{OA}(r)$, $\mathit{OB}(r)$ and the length of the arc $\stackrel{⌢}{\mathit{AB}}(l)$. In this, we substitute the value of \(l =\) $\mathrm{\pi }r$.

 

 

Perimeter of a semicircle = \(l+2r\) (where \(l=\pi r\)).

 

\(=\pi r + 2 r = (\pi + 2)r\) units.

The perimeter of a circular quadrant is defined as the sum of the two radii $\mathit{OA}(r)$, $\mathit{OB}(r)$ and the length of the arc $\stackrel{⌢}{\mathit{AB}}(l)$. In this, we substitute the value of \(l =\) $\frac{\mathrm{\pi }r}{2}$.

 

 

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.