Math Problem Statement

Find the total area of the irregularly shaped figure divided into labeled sections with different widths and heights.

Solution

The image you uploaded shows an irregularly shaped figure divided into smaller, labeled sections. Each section has its own width (shown horizontally) and height (shown vertically). To calculate the total area of the irregular shape, you can sum the areas of each rectangular section.

The labeled sections are as follows:

  1. First rectangle: Width = 1.5, Height = 2
  2. Second rectangle: Width = 1.75, Height = 2
  3. Third rectangle: Width = 1.75, Height = 3
  4. Fourth rectangle: Width = 2.75, Height = 3

The area of a rectangle is calculated by multiplying the width by the height. Let's calculate the area of each section.

Calculations:

  1. Area of first section = 1.5×2=31.5 \times 2 = 3
  2. Area of second section = 1.75×2=3.51.75 \times 2 = 3.5
  3. Area of third section = 1.75×3=5.251.75 \times 3 = 5.25
  4. Area of fourth section = 2.75×3=8.252.75 \times 3 = 8.25

Now, sum all the areas to get the total area: Total Area=3+3.5+5.25+8.25=20square units\text{Total Area} = 3 + 3.5 + 5.25 + 8.25 = 20 \, \text{square units}

The total area of the irregular shape is 20 square units.

Would you like further details or have any other questions?

Here are some related questions for further exploration:

  1. How do we calculate the area of other irregular shapes?
  2. Can we approximate areas of curves using a similar method?
  3. How does dividing a shape into rectangles affect area calculation accuracy?
  4. Can this method be extended to 3D shapes for volume calculation?
  5. What are other geometric methods for finding areas of irregular shapes?

Tip: When dealing with irregular shapes, dividing them into simple geometric figures like rectangles can help simplify area calculations.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area Calculation
Irregular Shapes

Formulas

Area of a rectangle: width × height

Theorems

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Suitable Grade Level

Grades 6-8