Question

The shape of a garden is rectangle length20m in the middle and semi circle 7m at the end .Find the area and the perimeter of the garden[length of rectangle is 20-(3.5+3.5)metres]

Answer 1

Answer:

Step-by-step explanation:

iven: Total length = 20 m

Diameter of semi circle = 7 m

Radius of semi circle =  = 3.5 m

Length of rectangular field

= 20 – (3.5 + 3.5) = 20 – 7 = 13 m

Breadth of the rectangular field = 7 m

Area of rectangular field =

= 13  7 = 91

Area of two semi circles =

=  = 38.5 m2

Area of garden = 91 + 38.5 = 129.5 m2

Now Perimeter of two semi circles =  = 22 m

And Perimeter of garden

= 22 + 13 + 13

= 48 m

Answer 2

$\bold{\underline{\underline{Answer:}}}$

Area of the garden = 129.5 m²

Perimeter of the garden = 48 m

$\bold{\underline{\underline{Step\:-\:by\:-\:step\:explanation:}}}$

Given :

• Length of a rectangular shaped garden = 20 m
• Semi circle in the middle of the rectangular garden = 7 m
• Length of rectangle = 20 - 7 = 13 m

To find :

• Area of rectangle
• Perimeter of the garden

Solution :

Diameter of the semi circle = 7 m

•°• Radius = $\bold{\frac{Diameter}{2}}$

Radius = $\bold{\frac{7}{2}}$

•°• Radius = 3.5 m

Breadth of the rectangular field is twice the radius of the semi circle.

•°• Breadth = 2(3.5) = 7 m

We have the length and breadth of the rectangular garden.

•°• We can calculate the area of the rectangular garden.

$\bold{Area\:of\:rectangular\:graden\:=\:l\times\:b}$

$\bold{Area\:of\:rectangular\:graden\:=\:13\times\:7}$

$\bold{Area\:of\:rectangular\:graden\:=\:91\:sq.m}$

Area of rectangular garden = 91m²

Now, let's calculate the area of the semi circle.

A rectangle has two ends. As mentioned in the question : semi circle 7m at the end.

•°• We infer that there are two semi circle formed each of radius = 3.5 m

We know that the area of the semi circle is calculated using the formula :-

$\bold{\boxed{Area\:of\:a\:semi\:circle\:=\frac{\pi\:r^2}{2}}}$

π = 3.14

r = 3.5 m

$\bold{Area\:of\:a\:semi\:circle\:={\frac{1}{2}}{\times\:3.14\times\:3.5^2}}$

$\bold{Area\:of\:a\:semi\:circle\:={\frac{1}{2}}{\times\:3.14\times\:3.5\times\:3.5}}$

$\bold{Area\:of\:a\:semi\:circle\:={\frac{1}{2}}{\times\:3.14\times\:12.25}}$

$\bold{Area\:of\:a\:semi\:circle\:={\frac{1}{2}}{\times\:38.465}}$

$\bold{Area\:of\:semi\:circle\:=\:19.25}$ (approx.)

Area of two semi circle will be twice the area of one semi circle.

Area of two semi circle = 2(19.25)

Area of two semi circle = 38.5 m²

Now, perimeter of semi circle,

$\bold{\frac{1}{2}}{\times\:2\times\pi\:\times\:3.5}$

$\bold{\frac{1}{2}}{\times\:2\times\:3.14\times\:3.5}$

= $\bold{3.14\times\:3.5}$

Perimeter of semi circle = 11 m

Perimeter of two semi circle = 2(11) = 22 m

Now, let's calculate the area of the garden

$\bold{\boxed{Area\:of\:garden\:=\:Area\:of\:rectangle\:+\:Area\:of\:two\:semi\:circle}}$

$\bold{Area\:of\:garden\:=\:91\:+38.5}$

$\bold{Area\:of\:garden\:=\:129.5\:sq.m}$

•°• Area of garden = 129.5 m²

Now, we will calculate the perimeter of the garden, which will be the sum of perimeter of the two semi circle and twice of length of the rectangle.

Perimeter of garden = $\bold{22+\:26}$

Perimeter of garden = $\bold{48\:m}$