Math Problem Statement

Find the area of the shaded polygon shown in the grid.

Solution

To calculate the area of the shaded polygon:

Steps:

  1. Count Full Squares: Identify all full grid squares completely inside the shaded polygon.
  2. 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.
  3. 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