Math Problem Statement

The grid you see below is in the shape of a rectangle. What is the area, in square units, of the shaded part?

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:

  1. The grid is made of 6 equal rectangles (2 columns and 3 rows).
  2. The shaded area forms a triangle in the top-left corner of the grid, spanning across two of the rectangles.
  3. 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:

Shaded Area=26×12=16×2=1 square unit.\text{Shaded Area} = \frac{2}{6} \times \frac{1}{2} = \frac{1}{6} \times 2 = 1 \text{ square unit}.

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:

  1. How do you calculate the area of a triangle given its base and height?
  2. What is the total area of the entire grid?
  3. How would the area change if the grid were composed of 4 rows and 2 columns?
  4. Can you apply this method to find the area of irregular shapes formed by diagonal lines?
  5. 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