Math, asked by ashmitbhati7, 20 days ago

if the perimeter of a protractor is 72cm , calculate its area

Answers

Answered by ItzMeMukku

$\textbf\color{red}{We know that shape of a protracter is semicircle,}$

$\\ \\$ $\sf\color{blue}{Let\: radius \:of \:the \:semicircle}$

$\underline{\boxed{\sf\purple{= r\: cm}}}$

$\sf\color{blue}{Perimeter \:of \:the\: protracter}$ $\underline{\boxed{\sf\purple{= 72 \:cm}}}$

$\\ \\$ $\sf{πr + 2r = 72}$

$\\ \\$ $\sf{r ( π + 2 ) = 72}$

$\\ \\$ $\sf{r ( 22/7 + 2 ) = 72}$

$\\ \\$ $\sf{r ( 22 + 14 )/7 = 72}$

$\\ \\$ $\sf{( 36/7 )r = 72}$

$\\ \\$ $\sf{r = ( 72 × 7 )/36}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ $\pink{\bigstar}★ \large\underline{\boxed{\bf\green{r\: = 14\: cm.}}}$

$\large\bf{\underline{\underline{Therefore}}}$

Area of the protracter = area of the semicircle

$\\ \\$ $\sf{= ( 22/7 ) (14)²/ 2}$

$\\ \\$ $\sf{= ( 22 × 14 × 14 )/( 7 × 2 )}$

$\\ \\$ $\sf{= 22 × 14}$

$\red{\bf {=\: 308\: cm²}}$

Thankyou :)

Refer attachment for better understanding :)

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