Math Problem Statement
Solution
The image shows a grid consisting of six equal rectangles, and the problem asks for the area of the shaded part of the grid.
To calculate this:
- The grid is made of 6 equal rectangles (2 columns and 3 rows).
- The shaded area forms a triangle in the top-left corner of the grid, spanning across two of the rectangles.
- This triangle is formed by a diagonal line running from the top-left corner to the bottom-right corner, cutting through two rectangles.
The shaded triangle is half of the upper two rectangles (because the diagonal cuts through the midpoints of these two rectangles).
Since there are 6 total rectangles, and the shaded region is half of 2 rectangles, the area of the shaded region is:
Thus, the area of the shaded part is 1 square unit.
Would you like more details or have any questions?
Here are five related questions:
- How do you calculate the area of a triangle given its base and height?
- What is the total area of the entire grid?
- How would the area change if the grid were composed of 4 rows and 2 columns?
- Can you apply this method to find the area of irregular shapes formed by diagonal lines?
- How can you verify the area of the shaded region by dividing it into smaller shapes?
Tip: When solving area problems involving diagonals, visualize how the shapes are split into simpler geometric figures like triangles or rectangles.
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Math Problem Analysis
Mathematical Concepts
Geometry
Area of triangles
Fractions
Formulas
Area of a triangle = 1/2 * base * height
Theorems
Area of a rectangle
Triangle area division theorem
Suitable Grade Level
Grades 6-8
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