Math Problem Statement

Find the perimeter of the shape below. Use π = 3.14. You may use a calculator on this problem, HOWEVER, show ALL your work….this means write down EVERYTHING you enter into the calculator! LABEL your answer…make sure to put one space between your number answer and your label.

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:

  1. 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 C=π×dC = \pi \times d, where dd is the diameter.
    • The circumference of one semicircle is half of this: Circumference of semicircle=π×d2\text{Circumference of semicircle} = \frac{\pi \times d}{2}.
    • For one semicircle: 3.14×1.82=2.826m\frac{3.14 \times 1.8}{2} = 2.826 \, \text{m}.
    • For both semicircles (since there are two), the total curved part is 2×2.826=5.652m2 \times 2.826 = 5.652 \, \text{m}.
  2. 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).
  3. 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 P=2×length of rectangle+total semicircle circumferenceP = 2 \times \text{length of rectangle} + \text{total semicircle circumference}.
    • So, P=2×6m+5.652m=12+5.652=17.652mP = 2 \times 6 \, \text{m} + 5.652 \, \text{m} = 12 + 5.652 = 17.652 \, \text{m}.

Final Answer:

The perimeter is approximately 17.65 m.

Would you like more details or have any questions?


Here are five related questions:

  1. How do we calculate the area of this shape?
  2. What would happen to the perimeter if the diameter of the semicircles doubled?
  3. How do you find the circumference of a circle if only the radius is given?
  4. How can we use a calculator to check this work?
  5. 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