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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 the perimeter of this garden. [Length of rectangle is 20 – (3.5 3.5) metres.]?
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Given:
- Length of the rectangle = 20 - (3.5 + 3.5) = 20 - 7 = 13 meters

To find:
- Area and perimeter of the garden

Steps to find the area:
1. Calculate the area of the rectangular part.
- Length of the rectangle = 13 meters
- Width of the rectangle is not given, so we cannot calculate the area of the rectangle.

2. Calculate the area of the semi-circular parts.
- The garden has two semi-circular ends.
- The radius of each semi-circle is half of the width of the rectangle.
- Width of the rectangle = 3.5 meters
- Radius of each semi-circle = 3.5/2 = 1.75 meters

- Area of each semi-circle = π * radius^2 / 2
= π * (1.75)^2 / 2
= π * 3.0625 / 2
= 4.8281 meters^2 (approx.)

3. Find the total area of the garden.
- The garden consists of one rectangular part and two semi-circular parts.
- Total area = Area of rectangular part + 2 * Area of semi-circular part
- Total area = 13 * (3.5 + 4.8281)
- Total area = 13 * 8.3281
- Total area = 108.2653 meters^2 (approx.)

Steps to find the perimeter:
1. Calculate the perimeter of the rectangular part.
- Perimeter of a rectangle = 2 * (Length + Width)
- Perimeter of the rectangular part = 2 * (13 + 3.5)
- Perimeter of the rectangular part = 2 * 16.5
- Perimeter of the rectangular part = 33 meters

2. Calculate the circumference of the semi-circular parts.
- Circumference of a circle = 2 * π * radius
- Circumference of each semi-circle = 2 * π * 1.75
- Circumference of each semi-circle = 3.5π meters

3. Find the total perimeter of the garden.
- The garden consists of one rectangular part and two semi-circular parts.
- Total perimeter = Perimeter of rectangular part + 2 * Circumference of semi-circular part
- Total perimeter = 33 + 2 * (3.5π)
- Total perimeter ≈ 33 + 21.99145
- Total perimeter ≈ 54.99145 meters

Answer:
- The area of the garden is approximately 108.2653 square meters.
- The perimeter of the garden is approximately 54.99145 meters.
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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 the perimeter of this garden. [Length of rectangle is 20 – (3.5 3.5) metres.]?
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