Math Problem Statement

Find the area of the shape in the image.

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:

  1. Count the Squares: Each small square on the grid represents a unit area (1 square unit).

  2. 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.

  3. 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 2×3=62 \times 3 = 6 square units.
  4. 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: Total Area=2+6+2=10 square units.\text{Total Area} = 2 + 6 + 2 = 10 \text{ square units}.

Would you like more details or have any questions?

Related Questions:

  1. What is the formula for the area of a triangle?
  2. How can you calculate the area of a complex shape by decomposing it?
  3. What would the area be if one of the triangles was larger?
  4. How do you calculate the area of shapes on a grid when dealing with partial squares?
  5. 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