Math Problem Statement
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:
-
Area of the larger rectangle (light shaded region):
- The larger rectangle has dimensions of 15 ft by 8 ft.
- Its area = .
-
Area of the smaller rectangle (white unshaded region):
- The smaller rectangle has dimensions of 6 ft by 4 ft.
- Its area = .
-
Area of the shaded region:
- The area of the shaded region is the difference between the larger rectangle and the smaller rectangle.
- Shaded area = .
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:
- How would you calculate the perimeter of the shaded region?
- If the units were in meters instead of feet, how would that change the result?
- How does subtracting areas differ from adding areas in composite shapes?
- What would happen if the smaller rectangle's dimensions were different?
- 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
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