Math Problem Statement
Solution
To find the area of the shaded region, follow these steps:
-
Calculate the area of the larger rectangle:
- The dimensions are given as (width) and (height).
- Area of the larger rectangle = .
-
Calculate the area of the inner (unshaded) square:
- The dimensions are .
- Area of the inner square = .
-
Subtract the area of the inner square from the larger rectangle:
- Area of the shaded region = .
Thus, the area of the shaded region is 104 square feet.
Would you like further details or have any questions?
Here are 5 related questions to expand your understanding:
- How do you calculate the area of composite shapes that include circles?
- What would the shaded area be if the inner square had different dimensions?
- How would the solution change if the outer shape were a circle instead of a rectangle?
- Can you derive a formula for the shaded area if only the dimensions are given symbolically?
- How do perimeter calculations differ from area calculations in such problems?
Tip: Always ensure you subtract the area of the inner shape from the outer shape to get the shaded area correctly.
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Math Problem Analysis
Mathematical Concepts
Geometry
Area Calculation
Subtraction of Areas
Formulas
Area of a rectangle = width × height
Area of a square = side × side
Shaded area = Area of larger shape - Area of inner shape
Theorems
Basic Area Theorem
Suitable Grade Level
Grades 6-8
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