Math Problem Statement

Find the area of the darker shaded region with the following measurements: 15 ft, 8 ft, 6 ft, and 4 ft.

Solution

To find the area of the darker shaded region in the image, we'll use the dimensions provided in the diagram. The darker shaded region is a rectangle with the following dimensions:

  • Width = 8 ft
  • Height = 6 ft

Step-by-step calculation:

  1. Area of the larger rectangle (light shaded region):

    • The larger rectangle has dimensions of 15 ft by 8 ft.
    • Its area = 15×8=120 square feet15 \times 8 = 120 \text{ square feet}.
  2. Area of the smaller rectangle (white unshaded region):

    • The smaller rectangle has dimensions of 6 ft by 4 ft.
    • Its area = 6×4=24 square feet6 \times 4 = 24 \text{ square feet}.
  3. Area of the shaded region:

    • The area of the shaded region is the difference between the larger rectangle and the smaller rectangle.
    • Shaded area = 12024=96 square feet120 - 24 = 96 \text{ square feet}.

Therefore, the area of the darker shaded region is 96 square feet.

Would you like more details on this, or have any other questions?

Here are 5 related questions to explore further:

  1. How would you calculate the perimeter of the shaded region?
  2. If the units were in meters instead of feet, how would that change the result?
  3. How does subtracting areas differ from adding areas in composite shapes?
  4. What would happen if the smaller rectangle's dimensions were different?
  5. Could we solve this using a different method, such as dividing the figure into smaller shapes?

Tip: Always verify the units you're working with in geometry problems, as they can influence your final answer significantly.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area of Composite Shapes
Rectangles

Formulas

Area of a rectangle = width × height

Theorems

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Suitable Grade Level

Grade 6-8