https://file.aiquickdraw.com/mathbot/file/1726784655609dmg4vqa2.jpg

To find the area of the shaded region, we will follow these steps:

1. **Find the area of the right triangle:**
   - The right triangle has a base and a height, both measuring 4 yards (yd).
   - The area of a triangle is given by the formula:
     \[
     A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height}
     \]
     \[
     A_{\text{triangle}} = \frac{1}{2} \times 4 \, \text{yd} \times 4 \, \text{yd} = 8 \, \text{yd}^2
     \]

2. **Find the area of the rectangle:**
   - The rectangle has a length of 4 yards and a width of 2 yards.
   - The area of the rectangle is given by:
     \[
     A_{\text{rectangle}} = \text{length} \times \text{width}
     \]
     \[
     A_{\text{rectangle}} = 4 \, \text{yd} \times 2 \, \text{yd} = 8 \, \text{yd}^2
     \]

3. **Subtract the area of the rectangle from the area of the triangle to find the area of the shaded region:**
   \[
   A_{\text{shaded}} = A_{\text{triangle}} - A_{\text{rectangle}} = 8 \, \text{yd}^2 - 8 \, \text{yd}^2 = 0 \, \text{yd}^2
   \]

Thus, the area of the shaded region is **0 square yards**.

Would you like more details or have any questions about this solution? Here are some related questions to expand your understanding:

1. How would the area change if the rectangle had different dimensions?
2. What is the formula for finding the area of a right triangle in terms of its base and height?
3. Can you find the perimeter of the shaded region?
4. How would the calculation change if the triangle was not a right triangle?
5. Can the area of a region ever be negative?

**Tip:** Always check that all parts of the diagram are properly measured and labeled before solving for areas.

A rectangle is removed from a right triangle to create the shaded region shown below. Find the area of the shaded region. Be sure to include the correct unit in your answer.

Learn how to find the area of a shaded region created by removing a rectangle from a right triangle. This problem involves key geometric concepts such as calculating the area of triangles and rectangles. Suitable for students in Grades 6-8.

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