Question

The perimeter of a sector of a circle of radius 5.2cm is 16.4cm. Find the area of the sector​

Answer 1

$\huge\sf\red{\underline{\underline{Given}}}\::$

$\begin{cases}\sf\gray{Perimeter \ of \ sector \ of \ circle \ = \ 16.4 \ cm} \\ \sf\gray{Radius \ of \ circle \ = \ 5.2 \ cm}\end{cases}$

$\huge\sf\blue{\underline{\underline{To\:Find}}}\::$

$\begin{cases}\sf\gray{The \ Area \ of \ sector}\end{cases}$

$\huge\sf\pink{\underline{\underline{Solution}}}\::$

$\sf\underline\orange{The \ length \ of \ arc} \ :$

$\mapsto\:\:\:\sf{\purple{ 5.2 \ + \ 5.2 \ + \ l \ = \ 16.4}} \\ \\ \sf\mapsto\:\:\:\sf{\green{ 10.4 \ + \ l \ = \ 16.4}} \\ \\ \sf\mapsto\:\:\:\sf{\purple{ l \ = \ 16.4 \ - \ 10.4}} \\ \\ \sf\mapsto\:\:\:\sf{\underline{\pink{ l \ = \ 6cm}}}$

$\star\:\:\sf{\red{Length \ of \ arc \ = 6cm}}$

$\sf\underline\orange{The \ Area \ of \ sector} \ :$

$\boxed{\bf{\pink{Area\:of\: sector=\dfrac{1}{2} radius\times length\:of\:arc}}}$

$\sf\hookrightarrow\:\:\:\sf{\purple{ Area=\dfrac{1}{\cancel2}\times 5.2\times \cancel{6}}} \\ \\ \sf\hookrightarrow\:\:\:\sf{\green{ Area=5.2\times 3}} \\ \\ \sf\hookrightarrow\:\:\:\sf{\pink{ Area\:of\:sector=15.6cm{}^{2}}}$

$\star\:\:\sf{\underline{\underline{\red{Hence,\:The\:area\:of\:sector\: is \: 15.6cm^{2} }}}}$