Question

If perimeter of a semi circular park is 72 metre find the area and radius​

Answer 1

Step-by-step explanation:

radius = 22.9 m

please refer to the image for detail explanation

Answer 2

$\star\small\sf\underline\blue{Given:-}$

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• The perimeter of a semi-circular park is 72 m.

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$\star\small\sf\underline\blue{Find \: Out:-}$

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• The area and radius of the semi-circular park = ?

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$\star\small\sf\underline\blue{Solution:-}$

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Perimeter of semi-circular park = 72m

$\implies \sf \: r \bigg(\pi + 2 \bigg) = 72 \: m \\ \\ \implies \sf \: r \bigg( \dfrac{22}{7} + \dfrac{2}{1} \bigg) = 72 \: m \\ \\ \implies \sf \: r \bigg( \dfrac{22 + 14}{7} \bigg) = 72 \: m \\ \\ \implies \sf \: r \times \dfrac{36}{7} = 72 \: m \\ \\ \therefore \sf \: Radius = \dfrac{ \cancel{72} \times 7}{ \cancel{36} } \\ \\ \leadsto\sf \: Radius = 2 \times 7 \\ \\ \leadsto \sf \: Radius = \boxed{ \bf \: 14 \: m}$

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$\star\small\sf\underline\blue{Therefore:-}$

• Radius of semi-circular park = 14 m

$\footnotesize\bold{\underline{\underline{\sf{\red{Now:-}}}}}$

$\sf \: Area = \dfrac{1}{2} \pi \: r {}^{2} \\ \\ \sf \: Area = \dfrac{1}{2} \times \dfrac{22}{7} \times (14) {}^{2} \\ \\ \sf \: Area = \dfrac{1}{ 2} \times \dfrac{22}{ \cancel7} \times \cancel{14 }\times 14 \\ \\ \sf \: Area = \dfrac{1}{ \cancel2} \times 22 \times \cancel2 \times 14 \\ \\ \sf \: Area =22 \times 14 \\ \\ \sf \: Area = \boxed{ \bf \: 308 \: m {}^{2} }$

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$\star\small\sf\underline\blue{Therefore:-}$

• Area of semi-circular park = 308 m²