Question

6. If the perimeter of a semi-circular park is 72 m, find its area..........
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Answer 1

The circumference of the semi circular park is 72 m.

$\sf \: \pi r = 72 \\ \implies \sf \: 3.14r = 72 \\ \implies \sf \: r = 22.9 \\ \implies \sf \: r \sim23 \: m$

Area of the semi circular park will be :

$\sf \: A = \dfrac{1}{2} {\pi r}^{2} \\ \\ \implies \sf \: A = \dfrac{1}{2} \times 3.14 \times (23) {}^{2} \\ \\ \implies \sf \: A = 1.57 \times 529 \\ \\ \implies \sf \: A = 830.53 \: {m}^{2}$

Therefore, area of the semi circular park is 850 m².

Answer 2

$\Large{\boxed{\underline{\overline{\mathfrak{\star \: Question :- \: \star}}}}}$

❥ If the perimeter of a semi-circular park is 72 m, find its area and radius

$\Large{\underline{\underline{\bf{AnSweR:-}}}}$

➪ The radius of the semi circular park is 14 meter.

➪ The area of the semi circular park is 307.72 square meter.

$\Large{\underline{\underline{\bf{GiVen:-}}}}$

➪ If the perimeter of semi circular park is 72 m.

$\Large{\underline{\underline{\bf{To find :-}}}}$

➪ The area and radius of the semi circle ?

$\Large{\underline{\underline{\bf{SoLuTioN:-}}}}$

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➪

$\large{\boxed{\bold{Perimeter\:of\: Semi\:park\:=\:P\:=\:2r\:+\:πr}}}$

We have given,

✒ P = 72

$\bf{\longmapsto P = r ( 2 + π ) }$

$\bf{\longmapsto 72 = r ( 2 + 3.14 ) }$

$\bf{\longmapsto 72 = r ( 5.14 ) }$

$\sf{\longmapsto r = \dfrac{72}{5.14}}$

$\bf{\longmapsto r = 14m }$

✒ The radius of the semi circular park is 14 meter.

$\large{\boxed{\bold{Area\:of\: Semi\:park\:=\:A\:=\:πr²\: ÷ \:2}}}$

$A \: = \: 3.14 \: × \: \frac{{14}^{2}}{2} \\ </p><p>A \: = \: 3.14 \: × \: \frac{196}{2} \\ </p><p>A \: = \: 3.14 \: × \: 98 \\ </p><p>A \: = \: 307. 72 m² \\ </p><p>$

$\therefore\underline{\boxed{\textsf{A= {\textbf{307.72m²}}}}} \qquad\qquad \bigg\lgroup\bold{Area \ of \ the \ park } \bigg\rgroup$

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☞ Formula required :-

$\large{\boxed{\bold{Perimeter\:of\: Semi\:park\:=\:P\:=\:2r\:+\:πr}}}$

$\large{\boxed{\bold{Area\:of\: Semi\:park\:=\:A\:=\:πr²\: ÷ \:2}}}$