Math Problem Statement

Find the perimeter of the figure shown above. (The figure is not drawn to scale and remember to use π ≈ 3.14 for all calculations involving π).

Solution

To find the perimeter of this trapezoid, we need to add the lengths of all four sides. Based on the image, the given sides are:

  • Top side = 67 meters
  • Bottom side = 61 meters
  • Left side = 58 meters
  • Right side = also 58 meters (since it’s a trapezoid and the non-parallel sides are typically equal).

Step-by-Step Solution

  1. Sum of All Sides (Perimeter): Perimeter=67+61+58+58\text{Perimeter} = 67 + 61 + 58 + 58 Calculating this: =244meters= 244 \, \text{meters}

Conversion to Decimeters

Since 1meter=10decimeters1 \, \text{meter} = 10 \, \text{decimeters}, we convert the perimeter from meters to decimeters:

244×10=2440dm244 \times 10 = 2440 \, \text{dm}

Final Answers

  • Perimeter = 244 meters
  • Perimeter = 2440 decimeters

Let me know if you'd like a more detailed explanation of each step or if you have further questions!

Here are some related questions:

  1. How would you find the area of this trapezoid if given the height?
  2. If one of the sides was missing, how could you determine it with only the perimeter?
  3. What if the shape was a parallelogram instead? How would that change the approach?
  4. How would the perimeter change if each side was increased by a fixed percentage?
  5. How can you convert between various metric units easily for such perimeter problems?

Tip: For unit conversions, always remember the power of 10 relationship in the metric system (e.g., meters to decimeters is ×10\times 10).

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Math Problem Analysis

Mathematical Concepts

Perimeter calculation
Basic geometry
Unit conversion

Formulas

Perimeter of a quadrilateral: P = side1 + side2 + side3 + side4
Meter to decimeter conversion: 1 m = 10 dm

Theorems

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Suitable Grade Level

Grades 6-8