Question

The perimeter of a sector of a circle of radius $5.7m$ is $27.2m$. Find the area of the sector.

Answer 1

$\Rightarrow$ Let $OAB$ be the given sector.

$\Rightarrow$ And $arcAB=l$

$\Rightarrow$ Perimeter of sector $OAB=OA+OB+arcAB$

$\therefore$ $27.2=5.7+5.7+l$

$\therefore$ $l=27.2-11.4=15.8cm$

$\Rightarrow$ Now, Area of sector $OAB=\frac{1}{2}\times l\times r$

$\therefore$ Area of sector $OAB=\frac{1}{2}\times 15.8\times 5.7$

$\therefore$ Area of sector $OAB=45.03,c{m}^2$