Math Problem Statement

Find the perimeter of the figure below. All lines meet at right angles.

Solution

To find the perimeter of this irregular figure, let's analyze the labeled lengths:

  1. The figure has several sides, meeting at right angles.
  2. Label each side as follows:
    • Vertical sides: 52 cm, 27 cm, and an unlabeled small segment (which can be calculated).
    • Horizontal sides: 25 cm, 27 cm, 20 cm, and an unlabeled small segment (which can be calculated).

Step 1: Determine the Missing Side Lengths

Since opposite sides in this stepped shape are equal:

  • The vertical side missing segment = 5227=25cm52 - 27 = 25 \, \text{cm}.
  • The horizontal side missing segment = 2720=7cm27 - 20 = 7 \, \text{cm}.

Step 2: Calculate the Perimeter

Now, sum up all side lengths:

  1. Vertical sides: 52+27+25=104cm52 + 27 + 25 = 104 \, \text{cm}
  2. Horizontal sides: 25+27+20+7=79cm25 + 27 + 20 + 7 = 79 \, \text{cm}

Total perimeter = 104+79=183cm104 + 79 = 183 \, \text{cm}.

Final Answer:

The perimeter of the figure is 183 cm.

Would you like more details or have any questions?


Related Questions:

  1. How to find perimeters of irregular shapes?
  2. How do right angles affect perimeter calculations?
  3. What is the perimeter formula for a rectangle?
  4. How to calculate missing sides in irregular polygons?
  5. Why is adding all side lengths necessary for perimeter?

Tip: Always check for missing side lengths by subtracting given lengths if the figure has symmetry or parallel sides.

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Math Problem Analysis

Mathematical Concepts

Geometry
Perimeter Calculation
Irregular Shapes

Formulas

Perimeter of an irregular shape = Sum of all side lengths

Theorems

Right Angle Properties

Suitable Grade Level

Grades 6-8