Question

The shape of a garden is rectangular in the middle and semi-circular at the ends. Find the area and the perimeter of this garden.
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Answer 1

Given :-

The shape of a garden is rectangular in the middle and semi-circular at the ends.

To Find :-

The area of the garden.

The perimeter of the garden.

Analysis :-

First we have to find the radius by dividing the diameter by 2.

Then find the length accordingly.

Using the formula of area of rectangle, find the area of the field.

Then find the area of 2 semi-circle and the garden.

Next using the values we have got, substitute and find the perimeter of 2 circles and garden.

Solution :-

We know that,

• l = Length
• b = Breadth
• d = Diameter
• r = Radius
• a = Area

Finding the radius,

$\underline{\boxed{\sf Radius=\dfrac{Diameter}{2} }}$

Given that,

Diameter of semi circle (d) = 7 m

Substituting them,

$\sf Radius=\dfrac{7}{2}=3.5 \ m$

Hence, the radius is 3.5 m.

Length of rectangular field,

$\sf = 20-(3.5+3.5)$

$\sf = 20-7 = 13 \ m$

Hence, the length of the field is 13 m.

By the formula,

$\underline{\boxed{\sf Area \ of \ rectangle=Length \times Breadth}}$

Given that,

Length (l) = 13 m

Breadth (b) = 7 m

Substituting their values,

Area = 13 × 7

Area = 91 m²

Therefore, the area is 91 m².

By the formula,

$\underline{\boxed{\sf Area \ of \ semi \ circle=2 \times \dfrac{1}{2} \times \pi r^{2}}}$

Given that,

Radius (r) = 3.5 m

By substituting,

$\sf =2 \times \dfrac{1}{2} \times \dfrac{22}{7} \times 3.5 \times 3.5$

$\sf =38.5 \ m^{2}$

Therefore, the area of 2 semi circle is 38.5 m².

Area of garden = Area of rectangular field + Area of two semi circles

Substituting their values,

Area of garden = 91 + 38.5

Area = 129.5 m²

Now,

Perimeter of two semi circles =  2πr

Substituting them,

$\sf =2 \times \dfrac{22}{7} \times 3.5=22 \ m$

Next,

Perimeter of garden = 22 + 13 + 13

Perimeter = 48 m