Question

if the perimeter of a semicircle Park is 72 metre find its area and radius​

Answer 1

Correct Question :

If the perimeter of a semicircle Park is 72 metre Find its area and radius

Given :

• Perimeter of Semi-Circle = 72 m

To Find :

• Area and Radius of Semicircle

Solution :

By using formula

$\purple{\boxed{ \bf{\sf \: Perimeter=πr+2r}}}$

$\rightarrow \: \: {\bf{\sf \:πr+2r=72m}}$

$\rightarrow{\bf{\sf \:r( \frac{22}{7} + 2) = 72}}$

$\rightarrow{\bf{\sf \:r( \frac{22 + 14}{7} ) = 72}}$

$\rightarrow{\bf{\sf \:r \times \frac{36}{7} = 72}}$

$\red {\boxed{\mathfrak{\rightarrow{\bf{\sf \:r = 14 \: m}}}}}$

By using Area Formula

${\boxed{ \bf{\sf \:Area = \frac{ {\pi \: r}^{2} }{2}}}}$

${ \bf{\sf \:➠ \: \: \: \frac{22}{7} \times \frac{14 \times 14}{2}}}$

${ \bf{\sf \:➠ \: \: 22 \times 14}}$

 

$\pink{\underline{\underline \frak{{308 \: m ²}}}}$

Answer 2

Given

• Perimetre of semi-circle= 72 metre

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To find

• area
• Radius

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Concept

~Here the concept of Perimetre and area of used. First we will find that radius of the semicircle using the Perimeter formula of semicircle then we will find the radius using area formula.

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Formula used

$\bull\bold \pink{Perimeter\:of\: semicircle=(πr)+2r}$

$\bull\bold\purple{Area \: of \: semi-circle= \frac{πr²}{2}}$

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Solution

$\sf{ \to \color{pink} \: Semicircle \: perimetre=πr +2r}$

$\sf{ \implies \: 72 = r(π+2)} \\ \\ \sf{ \implies r= \frac{72}{π+2}} \\ \\ \sf{ \implies r = \frac{72}{\frac{22}{7}+2}} \\ \\ \sf{ \implies r= \frac{72}{\frac{22+14}{7}}} \\ \\ \sf{ \implies r = \frac{72×7}{22+14}} \\ \\ \sf{\implies r =\frac{504}{36}} \\ \\ \sf{ \implies \color{red} r= 14 metre}$

Therfore the radius of semi-circle is 14 metre.

$\sf{ \implies Area\:of \: semicircle = \frac{πr²}{2}} \\ \\ \sf{ \implies Area \: of \: semicircle=\frac{\frac{22×14×14}{7}}{2}} \\ \\ \sf{ \implies \color{blue}Area \:of \: semicircle= 308 metre²}$

Therefore the area of semicircle is 308 m².

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More to know!!

✏️Area of the circle = πr²

✏️ circumference of circle= 2πr

✏️Area of Triangle= 1/2 ×base ×height

✏️Area of square = side ²

✏️Area of rectangle = length×breath

✏️ perimeter of square = 4 ×side

✏️perimeter of rectangle = 2(length×breath)

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