Find the area of the shaded polygon.
Understand the Problem
The question is asking for the area of a shaded polygon displayed on a grid. To determine the area, we may need to count the squares or apply a geometric formula depending on the shape.
Answer
The area of the polygon is $7$ square units.
Answer for screen readers
The area of the polygon is $7$ square units.
Steps to Solve
- Identify the shape and vertices of the polygon
The shape is a hexagon. We'll identify the vertices based on the grid. The hexagon has six sides.
- Count the unit squares completely inside the polygon
We can count the full squares that lie entirely within the outlined polygon. In this case, there are 6 complete unit squares inside the hexagon.
- Count the edges that are partially filled
Next, count the squares that are partially filled within the polygon. If there are any halves or quarters that contribute to the area, we will need to estimate them carefully.
- Total area calculation
The total area will be the sum of complete squares plus any partial squares counted as fractions.
Let’s assume we have identified 2 half squares that were partially inside the polygon. Each half square counts as $0.5$.
$$ \text{Total Area} = 6 + 2 \times 0.5 = 6 + 1 = 7 \text{ square units}$$
The area of the polygon is $7$ square units.
More Information
Counting the area of polygons can be approached by counting unit squares on a grid. Each complete square within the polygon contributes $1$ to the area, while partial squares may need to be added as fractions (e.g., $0.5$ for half squares).
Tips
- Overcounting or undercounting partial squares: It’s easy to misjudge how many partial squares are included, so make sure to carefully assess them.
- Misidentifying the polygon shape: Ensure the shape is accurately identified as this affects area calculations.
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