Question

The shape of a garden is rectangular in the middle and semi circular at the ends as shown in the diagram.Find the area and perimeter of the garden ​

Answer 1

Solution :

First refer to the attachment.

Given the garden is semi-circular at end.

$\rm \: Diameter \: of \: semi-circle = 7 m$

$\rm \: Radius \: of \: semi-circle = \dfrac{7}{2} = 3.5 \: m$

Since,It is semi-circle from both sides. Area would be :

$\bold{ \large{\boxed{\sf{Area = \blue{\: 2( \frac{1}{2} \pi {r}^{2}) }}}}}$

$\hookrightarrow \sf \: \pi {r}^{2} = \dfrac{22}{7} \times 3.5$

$\hookrightarrow \sf \: \dfrac{22}{7} \times \dfrac{35}{10} \times \dfrac{35}{10}$

$\hookrightarrow \large \boxed{ \sf \: 38.5 {m}^{2} }$

Now,Perimeter of 2 semi-circles

$\bold{ \large{\boxed{\sf{Perimeter = \red{\: 2\pi \: r }}}}}$

$\hookrightarrow \sf \: 2 \times \dfrac{22}{7} \times 3.5$

$\hookrightarrow \sf \large \boxed{ \sf \: 22 \: m}$

Let's move to the rectangular part now :

$\sf \: Length \: of \: rectangle = 20 - (3.5 + 3.5) \: m$

$\sf \: Length \: = 13 \: m$

$\sf \: Breadth \: of \: rectangle \: = 7 \: m$

$\bold{ \large{\boxed{\sf{Area = \purple{length \: \times \: breadth}}}}}$

$\hookrightarrow \sf \: (13 \times 7) {m}^{2}$

$\sf \large \boxed{ \sf \: 91 \: {m}^{2} }$

Now,Area of Garden =

$\sf \: 38.5 + 91 = \boxed{ \red{ \sf129.5 {m}^{2} }}$

Perimeter of the Garden =

2 × Circumference of Semi-Circle + 2 × length of rectangle

$\hookrightarrow\: \sf 2 \times 11 \times + 2 \times 13$

$\sf \: 22 + 26 = \boxed{ \red{ \sf 48 m }}$

Answer 2

✪$\huge{\boxed{\underline{\tt{\blue{Answer}}}}}$✪

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Given:

★ Diameter = 7 m

so radius = 3.5m

★ length of garden = 20m

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To find

Area and Perimeter of the garden

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SoluTion:

$\huge{\green{\boxed{Perimeter}}}$

Side of Rectangle

$20 - [3.5 + 3.5] \\ \\ \implies 20 - 7 \\ \leadsto\boxed{13m}$

Now We need circumference of the semi circles

These Two semi circles will make one full circle

Therefore,

Circumference of circle(2πr)

$\implies 2 \times \dfrac{22}{\cancel{7}} \times \cancel{3.5} \\ \implies \dfrac{\cancel{2} \times 22 }{\cancel{2}} \\ \leadsto{\boxed{22m}}$

$\large{\therefore Perimeter\:of\:the\:Garden} \\ \implies 13+13 + 22 \\ \huge\leadsto{\boxed{\boxed{\underline{48m}}}}$

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$\huge{\green{\boxed{Area}}}$

Area of Figure = Area of Circle + Area of Rectangle

Area of circle(πr²)

$\implies \dfrac{22}{7} \times (3.5)^2 \\ \implies \dfrac{22}{\cancel{7}} \times \cancel{3.5} \times 3.5 \\ \implies \dfrac{\cancel{22}}{\cancel{2}} \times 3.5 \\ \implies 11 \times 3.5\\ \leadsto\boxed{38.5}$

Area of Rectangle(L x B)

$13 \times 7 \\ \leadsto\boxed{91}$

Therefore

Area of Garden

$91 + 38.5 \\ \huge\leadsto{\boxed{\boxed{\underline{129.5}}}}$

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