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Given the problem, we need to find the area of the shaded region inside the square, which has a side length of 1 unit.

### Explanation:
1. **Square Properties**:
   - The square \( ABCD \) has a side length of 1 unit. Therefore, the area of the square is \( 1 \times 1 = 1 \) square unit.

2. **Line Intersection**:
   - The lines \( AC \) and \( BD \) intersect at the center of the square, which is point \( O \). Since the square has a side length of 1 unit, the coordinates of point \( O \) are \( \left( \frac{1}{2}, \frac{1}{2} \right) \).

3. **Triangle Analysis**:
   - Point \( M \) is the midpoint of side \( AB \), so \( M \) has coordinates \( \left( \frac{1}{2}, 0 \right) \).
   - The shaded region is a triangle with vertices \( A \), \( O \), and \( M \).

4. **Area of the Shaded Triangle \( \Delta AOM \)**:
   - The formula for the area of a triangle with vertices \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\) is:
     \[
     \text{Area} = \frac{1}{2} \left| x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2) \right|
     \]
   - Substituting the coordinates of points \( A(0, 0) \), \( O\left(\frac{1}{2}, \frac{1}{2}\right) \), and \( M\left(\frac{1}{2}, 0\right) \):
     \[
     \text{Area} = \frac{1}{2} \left| 0 \left(\frac{1}{2} - 0\right) + \frac{1}{2}(0 - 0) + \frac{1}{2}(0 - \frac{1}{2}) \right|
     \]
     \[
     = \frac{1}{2} \left| 0 + 0 - \frac{1}{8} \right| = \frac{1}{2} \times \frac{1}{8} = \frac{1}{16}
     \]

Hence, the area of the shaded region is \(\frac{1}{16}\) square units.

Would you like more details or have any questions?

### Related Questions:
1. How do you calculate the area of a triangle given its vertices?
2. What is the formula for the area of a square?
3. How do you find the midpoint of a line segment in a coordinate plane?
4. What is the relationship between diagonals in a square?
5. How does changing the side length of a square affect the area of shapes inside it?

### Tip:
When calculating the area of a triangle using vertices, always use the absolute value to ensure you get a positive result.

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Find the area of a shaded triangle inside a square with a side length of 1 unit. This solution uses geometric concepts, including triangle area calculation and midpoint properties. Suitable for students in Grades 7-9.

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