Math Problem Statement

Calculate the area of the entire composite shape formed by dissecting the rectangle into smaller sections as shown in the image.

Solution

The image shows a composite shape made by dissecting a rectangle into smaller sections, with various dimensions labeled. We have two different shapes that are part of a filling or dissection method problem.

Key dimensions:

  • The larger rectangle is 7 cm in height and 6 cm in width.
  • The inner shape is formed by a cut-out, creating two triangular sections with side lengths marked as 6 cm, 4 cm, and 3 cm.

It seems the goal of the problem is to calculate the area of the original shape (likely the entire rectangle) and the area of the dissected parts, possibly to find relationships between these areas or to reassemble the shape in a different way.

Would you like me to calculate the area of the entire rectangle and the dissected parts or clarify a specific part of this problem?


Here are 5 related questions to further explore:

  1. What is the total area of the original rectangle before dissection?
  2. How can we calculate the area of each triangular section individually?
  3. How do the areas of the dissected shapes compare to the original?
  4. Can the dissection method help us create other composite shapes with the same area?
  5. How is the concept of area conservation applied in filling or dissection methods?

Tip: When working with dissection problems, always check if shapes are rearranged or cut into simpler geometric forms to facilitate calculations.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area calculation
Dissection method

Formulas

Area of a rectangle: length × width
Area of a triangle: 0.5 × base × height

Theorems

Area conservation

Suitable Grade Level

Grades 5-7