Math Problem Statement

Find the shaded area of the rectangle. The rectangle has total dimensions of 6 units in height and 4 units in width, divided into 6 smaller sections. The shaded part represents 1 section.

Solution

The problem asks to find the shaded area of the rectangle shown in the image. Here's a step-by-step approach:

  1. Total dimensions of the rectangle:

    • The height of the entire rectangle is labeled as 6 units.
    • The width of the entire rectangle is labeled as 4 units.

    So, the total area of the rectangle can be calculated as: Total Area=6×4=24 square units.\text{Total Area} = 6 \times 4 = 24 \text{ square units.}

  2. Subdivision of the rectangle: The rectangle is divided into smaller parts. It consists of 6 smaller squares or rectangular sections (2 rows and 3 columns).

  3. Shaded portion: The shaded portion represents 1 out of the 6 sections of the rectangle. Since the entire rectangle is divided into 6 equal parts, the area of each part is: Area of one part=246=4 square units.\text{Area of one part} = \frac{24}{6} = 4 \text{ square units.}

Thus, the shaded area is 4 square units.

Let me know if you want further details or explanations.


Here are 5 related questions to extend this topic:

  1. How do you calculate the area of irregularly shaped figures?
  2. If the entire rectangle was divided into 12 smaller parts, what would the area of each part be?
  3. What is the perimeter of the entire rectangle?
  4. If the width of the rectangle were doubled, what would be the new area?
  5. How can you calculate the area of a triangle if it is part of a composite shape?

Tip: Always check the total dimensions and the number of divisions when working with shaded areas to avoid confusion.

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Math Problem Analysis

Mathematical Concepts

Area calculation
Rectangles
Division of areas

Formulas

Area of a rectangle: length × width
Area of each section: Total area / Number of sections

Theorems

Area theorem of rectangles

Suitable Grade Level

Grades 5-7