https://file.aiquickdraw.com/mathbot/file/17288965969287gv0b6o1.jpg

The problem asks how many small right-angled triangles (each shaped like the one marked "a" in the top left) are used to make the larger shaded trapezoid shape shown on the grid.

### Step-by-Step Solution:

1. **Analyze the small triangle "a"**: 
   - The small triangle "a" occupies half of a single square on the grid.
   - Its area is therefore half of the area of one square.

2. **Count the total number of squares in the trapezoid**:
   - By inspecting the grid, the shaded trapezoid appears to cover:
     - A base of 8 squares.
     - A top of 4 squares.
     - A height of 4 squares (counting from the bottom to the top of the trapezoid).

3. **Calculate the area of the trapezoid in terms of square units**:
   - The formula for the area of a trapezoid is:
     \[
     \text{Area} = \frac{1}{2} \times ( \text{Base 1} + \text{Base 2} ) \times \text{Height}
     \]
   - Substituting values:
     \[
     \text{Area} = \frac{1}{2} \times (8 + 4) \times 4 = \frac{1}{2} \times 12 \times 4 = 24 \text{ square units}
     \]

4. **Determine how many triangles fit into the trapezoid**:
   - Since each small triangle "a" has half the area of a square, and the trapezoid has an area of 24 square units, the number of small triangles is:
     \[
     \text{Number of triangles} = 24 \times 2 = 48
     \]

### Conclusion:
Thus, 48 small triangles are used to make the trapezoid. The correct answer is **D: 48 triangles**.

Would you like more details on any part of the solution or have any questions?

### Further Related Questions:
1. How would the number of triangles change if the trapezoid's height were doubled?
2. Can you derive the formula for the area of a trapezoid step-by-step?
3. How would the number of triangles change if the base of the trapezoid were reduced to 6 squares?
4. What is the relationship between the number of triangles and the total area in square units?
5. Could the shape be divided into other geometric figures apart from triangles?

### Tip:
When solving grid-based geometry problems, it helps to break complex shapes into simpler units (like squares or triangles) and use their areas to determine the solution.

How many triangles are used to make the shape below?

Solve a geometric problem by calculating how many small triangles form a trapezoid. This step-by-step guide covers grid-based geometry, the area of trapezoids, and triangle properties. Suitable for Grades 5-7.

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