Math Problem Statement

Answer Please

Find the perimeter of the given L-shaped figure with side lengths 45 m, 30 m, 25 m, and 60 m.

Solution

To find the perimeter of this shape, we need to add the lengths of all its outer edges.

The labeled dimensions are:

  • 45m45 \, m
  • 30m30 \, m
  • 25m25 \, m
  • 60m60 \, m

The shape is an L-shape, so it has both vertical and horizontal sides. Some of these sides are not labeled directly, but we can determine their lengths by subtracting other lengths.

  1. Total Horizontal Distance:

    • The bottom side is labeled 60m60 \, m.
    • The top horizontal part consists of two segments: one is 30m30 \, m (labeled), and the other is 6030=30m60 - 30 = 30 \, m.
  2. Total Vertical Distance:

    • The left side is labeled 45m45 \, m.
    • The right vertical side consists of two segments: 25m25 \, m (labeled) and 4525=20m45 - 25 = 20 \, m for the shorter right side.

Now, we add all outer segments: 45+30+20+25+30+60=210m45 + 30 + 20 + 25 + 30 + 60 = 210 \, m

So, the perimeter is: 210 m\textbf{210 m}

This matches the correct answer shown in red.


Would you like a step-by-step breakdown of this solution or any further clarification?

Here are five related questions to deepen your understanding:

  1. How would you calculate the area of this L-shaped figure?
  2. What if one side of the L-shape was unknown? How would you approach finding its perimeter?
  3. How can we verify the perimeter of composite shapes using smaller rectangles?
  4. What is the difference between calculating the perimeter and the area of a shape?
  5. Can you think of other shapes where subtraction helps in finding missing lengths?

Tip: When dealing with composite shapes, break them down into smaller parts to calculate unknown sides or other measurements accurately.

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Math Problem Analysis

Mathematical Concepts

Geometry
Perimeter Calculation
Composite Shapes

Formulas

Perimeter of Composite Shapes: Sum of all outer edges

Theorems

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Suitable Grade Level

Grade 5