Question

shape of Garden is rectangular in the middle and semi circular at the end is shown in figure find area and perimeter of this garden

Answer 1

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Find the area of two Semi Circle

We have given diameter of semi - circle = 7 m

So , it's radius would be 7/2 = 3.5 m

Area of  Semi - Circle = $\frac{1}{2} * \pi r^2$

So , Area of 2 Semi - Circle = $2(\frac{1}{2} * \pi r^2)$

=> $\pi r^2 = \frac{22}{7} * (3.5)^2$

=> $\frac{22}{7} * \frac{35}{10} * \frac{35}{10}$

=> $\frac{11\ * \ 35}{10}$

=> $\frac{385}{10}$

=> 38.5 m^2

Find the perimeter of 2  Semi - Circle

$2(\frac{\pi r^2}{2} )$

=> $2 \pi r$

=> $2 * \frac{22}{7} * (3.5)$

=> $2 * \frac{22}{7} * \frac{35}{10}$

=> 22 m

Find the area of  rectangle

Length of the rectangle = 20 - ( 3.5 + 3.5 ) m

=> 13 m

Breadth = 7m (given)

Area of rectangle = Length * Breadth

13 * 7

=> 91 m^2

Find Perimeter of rectangle

Perimeter of rectangle = 2* ( Length + Breadth )

=> 2 * ( 13 + 0)

=> 2 * 13

=> 26 m

Find Area of Garden

Area of Garden = Area of 2 Semi Circle + Area of the rectangle

$(38.5 + 91) m^2$

=> $129.5 \ m^2$

Find the Perimeter of the Garden

Perimeter of the garden = Perimeter of 2 Semi-Circle + perimeter of rectangle

=> 22 + 26

=> 48 m

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Answer 2

Given:

• Total length = 20 m
• Diameter of the semi circle = 7 m

To Find:

• The area from the given figure.
• The perimeter of the given figure.

Solution:

Total length = 20 m

Diameter of the semi circle = 7 m

So,

∴ Radius of a semi circle = $\frac{7}{2}= 3.5 \: m$

Length of rectangular field:

$:\implies 20-(3.5 + 3.5) = 20-7\\:\implies 13 \:m$

Breadth of the rectangular field = 7 m

Area of the rectangular field = l × b

$:\implies 13 \times 7 = 91m^{2}$

Now,

Area of two semi circles = $2 \times \frac{1}{2} \times \pi \times r^{2}$

$= 2 \times \frac{1}{2} \times \frac{22}{7} \times 3.5 \times 3.5\\ :\implies 38.5 \: m^{2}$

Finding the area,

Area of the garden = $91 + 38.5 = \boxed{ 129.5 \: m^{2}}$

Now, the perimeter of two semi circle,

$= 2\pi r = 2 \times \frac{22}{7} \times 3.5 \times 3.5\\ \implies \boxed{22 \: m}$

Finding the perimeter,

Perimeter of the garden,

$=22 +13 +13\\:\implies \boxed{ 48 \: m}$