Math Problem Statement
Find the area of the shaded polygon shown in the grid.
Solution
To calculate the area of the shaded polygon:
Steps:
- Count Full Squares: Identify all full grid squares completely inside the shaded polygon.
- Estimate Partial Squares: For any squares that are partially inside, approximate their contribution to the total area. Typically, two half-squares combine to make one full square.
- Sum Up Contributions: Add the areas of full squares and partial squares.
From the image, the polygon is symmetric and can be broken into clear triangular and rectangular sections if the symmetry is used. I'll analyze this structure for precise results:
- Top and bottom triangles: Each has half the area of a rectangle (Complete doen prints )
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Math Problem Analysis
Mathematical Concepts
Geometry
Area calculation
Polygon properties
Formulas
Area approximation using grid units
Symmetry in polygons for area calculation
Theorems
Decomposition of shapes into triangles and rectangles
Suitable Grade Level
Grades 6-8