Question

The perimeter of a circular field is 44m. The area of the given circular field is

Answer 1

let r be the radius of the circular field
$2\pi \: r \: = 44$
$r = 7$
Area of the circular field
$= \pi {r}^{2} \\ = \frac{22}{7} \times 7 \times 7 \\ = 154 \: square \: m$

Answer 2

Given: Perimeter (Circumference) of circular field is 44 m

To find: Area of circular field?

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We know that,

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$\star\;{\boxed{\sf{\purple{Perimeter_{\;(circle)} = 2 \pi r}}}}$

$:\implies\sf 2 \times \dfrac{22}{7} \times r = 44\\ \\ :\implies\sf \dfrac{44}{7} \times r = 44\\ \\ :\implies\sf r = \cancel{44} \times \dfrac{7}{{\cancel 44}}\\ \\ :\implies\sf r = 7\\ \\ :\implies{\boxed{\sf{\pink{r = 7\;cm}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Radius\;of\; circular\;field\;is\; {\textsf{\textbf{7\;cm}}}.}}}$

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Area of circular field,

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$\star\;{\boxed{\sf{\purple{Area_{\;(circle)} = \pi r^2}}}}$

$:\implies\sf Area_{\;(field)} = \dfrac{22}{7} \times (7)^2\\ \\ :\implies\sf Area_{\;(field)} = \dfrac{22}{{\cancel 7}} \times {\cancel 7} \times 7\\ \\ :\implies{\boxed{\sf{\pink{Area_{\;(field)} = 154\;m^2\;}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\;Area\;of\; circular\;field\;is\; \bf{154\;m^2}.}}}$