Math Problem Statement

Find the perimeter of the figure below: (Take π = 3.14)

Solution

To find the perimeter of this figure, we need to calculate the perimeter of each part and then sum them up.

Breakdown of the Shape

The figure seems to consist of:

  1. Two vertical straight sides, each 18 meters in length.
  2. One horizontal straight side at the bottom, 6 meters in length.
  3. A semicircular arc at the top, which seems to be part of a circle with a diameter equal to the width of the shape (6 meters).

Step-by-Step Calculation

  1. Straight Edges:

    • The two vertical sides are each 18 m, so 2×18=362 \times 18 = 36 meters.
    • The bottom side is 6 m.
  2. Semicircular Arc:

    • The diameter of the semicircle is 6 m, so the radius r=62=3r = \frac{6}{2} = 3 meters.
    • The circumference of a full circle with this radius would be 2πr=2×3.14×3=18.842 \pi r = 2 \times 3.14 \times 3 = 18.84 meters.
    • Since we only have a semicircle, we take half of this: 18.842=9.42\frac{18.84}{2} = 9.42 meters.
  3. Adding All Parts Together:

    • Total perimeter = 36+6+9.42=51.4236 + 6 + 9.42 = 51.42 meters.

Final Answer:

The perimeter of the figure is 51.42 meters.

Would you like further details on any part of this solution?


Related Questions to Explore

  1. How would the perimeter change if the semicircular arc was a full circle?
  2. How is the perimeter of a closed shape different from the circumference of a circle?
  3. What would happen to the perimeter if the diameter of the semicircle were doubled?
  4. If only one side of the vertical or horizontal segments were missing, how would you calculate the perimeter?
  5. How would using a different value for π\pi (like 3.1416) affect the perimeter?

Tip

When calculating the perimeter of complex shapes, break them down into simpler components (like straight lines and arcs) for easier computation.

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Math Problem Analysis

Mathematical Concepts

Geometry
Perimeter
Arcs and Semicircles

Formulas

Perimeter of rectangle = 2 * (length + width)
Circumference of a circle = π * diameter
Perimeter of semicircle = (π * diameter) / 2

Theorems

Properties of a semicircle

Suitable Grade Level

Grades 6-8