Question

If the Perimeter of Semicircular Park is 72m.
Find it's Radius and Area !​

Answer 1

$\mathfrak{Answer : } \:$

★ Perimeter of semicircle = 72m

Let r be the radius of circle.

➡ 2πr/2 + 2r = 72

➡ πr + 2r = 72

➡ r = 72/π + 2

➡ r = 72/(22/7 + 2)

➡ r = 14m

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➡ Area of semicircle = πr²/2

➡ Area of semicircle = 22/7 * 14 * 14/2

➡ Area of semicircle = 308m²

★ The area and radius of circular park is 308m² and 14m.

Answer 2

AnswEr :

⠀

$\large \red{\boxed{ \bold{r = 14m \: ~and,~ Area = 308 {m}^{2} }}} \:$

⠀

Explanation :

▣ Given :

• Perimeter of Semicircular Park is 72m

▣ To Find :

• Find Radius and Area of Semicircular Park.

▣ Solution :

• Let the Radius be r.

$\boxed{ \bold{Perimeter \: of \: Semicircle = \frac{2\pi r}{2} + 2r }}$

$\Rightarrow \bold{Perimeter =( \pi + 2)r}$

$\Rightarrow \bold{72 = ( \large{\frac{22}{7} } + 2) \times r}$

$\Rightarrow \bold{72 = \large{\frac{(22 + 14)}{7}} \times r}$

$\Rightarrow \bold{72 = \large{ \frac{36}{7}} \times r}$

$\Rightarrow \bold{r = \large{\frac{(72 \times 7)}{36} }}$

$\Rightarrow \bold{r = 2 \times 7}$

$\Rightarrow \large\bold{r = 14m}$

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$\boxed{ \bold{Area \: of \: Semicircle = \large{ \frac{\pi {r}^{2} }{2} }}}$

$\Rightarrow \bold{Area = \large{ \frac{22}{7} \times 14 \times 14 \times \frac{1}{2} }}$

$\Rightarrow \bold{Area = 22 \times 2 \times 7}$

$\large\Rightarrow \bold{Area = 308 {m}^{2} }$

$\large\therefore$ Radius of Semicircular Park is 14m and Area is 308m².