Math Problem Statement
Solution
The problem asks for an expression representing the area of the shaded region. Here's how we can solve this:
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Area of the large square: The large square has a side length of . The area of this square is:
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Area of the smaller rectangle: The small rectangle has dimensions 5 (height) and 2 (width). The area of the rectangle is:
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Area of the shaded region: The shaded region is the area of the large square minus the area of the small rectangle:
Thus, the expression representing the area of the shaded region is:
Would you like more details or have any questions? Here are some related questions to expand the topic:
- How would the expression change if the dimensions of the small rectangle were different?
- What is the area of the shaded region if ?
- How would you express the perimeter of the large square in terms of ?
- What would happen to the shaded area if the rectangle's width doubled?
- How can this problem be generalized to any square with a smaller rectangle subtracted from it?
Tip: Always subtract the areas of removed parts when calculating the area of complex shapes.
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Math Problem Analysis
Mathematical Concepts
Geometry
Algebra
Area Calculation
Formulas
Area of a square = side^2
Area of a rectangle = length × width
Theorems
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Suitable Grade Level
Grades 7-9
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