Math Problem Statement
Solution
To calculate the area of the shape in the image, we can break it down into simpler geometric components based on the grid provided.
Step-by-Step Breakdown:
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Count the Squares: Each small square on the grid represents a unit area (1 square unit).
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Decompose the Shape: The shape resembles two triangles at the top and bottom, with a central rectangular region. We can estimate or directly count the number of full and partial squares in each section.
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Area Calculation by Regions:
- Top and Bottom Triangles: Each triangle seems to occupy 2 full squares based on the grid.
- Central Rectangular Region: The central rectangle spans 2 full rows vertically and 3 units horizontally, giving an area of square units.
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Total Area:
- Top Triangle: 2 square units
- Bottom Triangle: 2 square units
- Central Rectangle: 6 square units
So, the total area of the shape is:
Would you like more details or have any questions?
Related Questions:
- What is the formula for the area of a triangle?
- How can you calculate the area of a complex shape by decomposing it?
- What would the area be if one of the triangles was larger?
- How do you calculate the area of shapes on a grid when dealing with partial squares?
- Could symmetry help in determining the area of more complex polygons?
Tip: When working with composite shapes, breaking them into simpler components like rectangles, triangles, or squares can make the area calculation easier.
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Math Problem Analysis
Mathematical Concepts
Geometry
Area Calculation
Decomposition of Shapes
Formulas
Area of a rectangle: width × height
Area of a triangle: 1/2 × base × height
Theorems
Decomposing complex shapes into simpler ones
Suitable Grade Level
Grades 6-8