Math Problem Statement
Solution
To find the perimeter of this shape, we need to break it down into simpler components. The shape consists of two semicircles on either side of a rectangle.
Step-by-step solution:
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Calculate the circumference of the semicircles:
- The diameter of each semicircle is given as 1.8 m.
- The circumference of a full circle is given by , where is the diameter.
- The circumference of one semicircle is half of this: .
- For one semicircle: .
- For both semicircles (since there are two), the total curved part is .
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Calculate the length of the rectangle:
- The rectangle's length is 6 m, and its width is 1.8 m (matching the diameter of the semicircles).
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Perimeter of the entire shape:
- The perimeter consists of the curved part from the semicircles plus the lengths of the two sides of the rectangle.
- Total perimeter .
- So, .
Final Answer:
The perimeter is approximately 17.65 m.
Would you like more details or have any questions?
Here are five related questions:
- How do we calculate the area of this shape?
- What would happen to the perimeter if the diameter of the semicircles doubled?
- How do you find the circumference of a circle if only the radius is given?
- How can we use a calculator to check this work?
- How would the formula change if the shape were made from quarter circles instead of semicircles?
Tip: For shapes that combine straight lines and curves, break them into basic shapes like rectangles and circles to calculate perimeters easily.
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Math Problem Analysis
Mathematical Concepts
Perimeter
Circles
Rectangles
Geometry
Formulas
Circumference of a circle: C = π × d
Perimeter of a composite shape: Sum of all sides and curved parts
Theorems
Circumference formula
Suitable Grade Level
Grades 6-8
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