Math Problem Statement

This shape is made up of four rectangles. Determine the total perimeter of the shape.

Solution

To determine the total perimeter of the shape in the problem, we need to calculate the sum of all the outer edges of the shape. Let’s analyze the shape step by step using the dimensions provided in the diagram.

Step 1: Identify the dimensions of the outer edges

From the diagram:

  • The left vertical side is 15m+30m=45m15 \, \text{m} + 30 \, \text{m} = 45 \, \text{m}.
  • The right vertical side is 60m60 \, \text{m} (this is already labeled).
  • The top horizontal side is 8m+10m=18m8 \, \text{m} + 10 \, \text{m} = 18 \, \text{m}.
  • The bottom horizontal side is 10m10 \, \text{m}.

Step 2: Add the lengths of all the outer edges

Perimeter=(left vertical)+(right vertical)+(top horizontal)+(bottom horizontal)\text{Perimeter} = (\text{left vertical}) + (\text{right vertical}) + (\text{top horizontal}) + (\text{bottom horizontal}) Substitute the values: Perimeter=45m+60m+18m+10m\text{Perimeter} = 45 \, \text{m} + 60 \, \text{m} + 18 \, \text{m} + 10 \, \text{m}

Perimeter=133m\text{Perimeter} = 133 \, \text{m}

Final Answer:

The total perimeter of the shape is 133 meters.

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Math Problem Analysis

Mathematical Concepts

Perimeter
Geometry
Rectangles

Formulas

Perimeter = Sum of all outer edge lengths

Theorems

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Suitable Grade Level

Grades 6-8