Math Problem Statement

Find the perimeter of the figure below.

Solution

To find the perimeter of the figure, we need to add up the lengths of all the outer sides. Let's analyze each segment of the figure given:

  1. Top Horizontal Side: 19 m
  2. Left Vertical Side: 7 m
  3. Inner Horizontal Gap: 9 m (doesn't contribute to the outer perimeter)
  4. Right Vertical Side of the Gap: This length is not marked, but we can calculate it. It should be 128=4m12 - 8 = 4 \, \text{m}, because the total height on the right side is 12 m, and the inner vertical side is marked as 8 m.
  5. Right Vertical Side: 12 m
  6. Bottom Horizontal Side: 8 m
  7. Right Side of the Gap: 8 m

Now, we add up these lengths:

19+7+4+12+8+8=58m19 + 7 + 4 + 12 + 8 + 8 = 58 \, \text{m}

Thus, the perimeter of the figure is 58 meters.

Would you like further details, or do you have any questions?


Here are some additional questions related to this topic:

  1. How would the perimeter change if one of the side lengths were increased by a certain amount?
  2. What is the difference between finding the perimeter and the area of a shape?
  3. How do you find the perimeter of irregular shapes like this one?
  4. Can the perimeter be calculated differently if any of the sides are unknown?
  5. How would you approach calculating the perimeter if this figure was a 3D object?

Tip: For composite shapes, break down the figure into simpler parts to identify each dimension clearly before summing up the perimeter.

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Math Problem Analysis

Mathematical Concepts

Perimeter
Addition of Measurements
Geometry

Formulas

Perimeter = Sum of all outer side lengths

Theorems

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Suitable Grade Level

Grades 6-8