https://file.aiquickdraw.com/mathbot/file/1727402416119r779zjan.jpg

To find the area of the shaded region in the parallelogram, let's break down the problem step by step.

1. **Understanding the diagram**:
   - The parallelogram is given with a base of 12 cm.
   - There's a height indicated on the right side of the parallelogram as 4 cm.
   - On the left, a right triangle is formed with legs of 5 cm and 4 cm.
   - The shaded region represents the part of the parallelogram that we need to find the area for.

2. **Formula for the area of the parallelogram**:
   The area of the entire parallelogram is calculated using the formula:
   \[
   \text{Area} = \text{base} \times \text{height}
   \]
   Substituting the given values:
   \[
   \text{Area of parallelogram} = 12 \, \text{cm} \times 4 \, \text{cm} = 48 \, \text{cm}^2
   \]

3. **Finding the area of the unshaded triangle**:
   On the left side, there is a right-angled triangle with a base of 5 cm and a height of 4 cm. The area of a triangle is given by:
   \[
   \text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height}
   \]
   Substituting the values:
   \[
   \text{Area of triangle} = \frac{1}{2} \times 5 \, \text{cm} \times 4 \, \text{cm} = 10 \, \text{cm}^2
   \]

4. **Finding the area of the shaded part**:
   The shaded area is the difference between the total area of the parallelogram and the area of the triangle:
   \[
   \text{Shaded area} = 48 \, \text{cm}^2 - 10 \, \text{cm}^2 = 38 \, \text{cm}^2
   \]

So, the area of the shaded part is **38 cm²**.

Let me know if you need further explanation or details! Here are 5 related questions to deepen your understanding:

1. How do you calculate the area of a trapezoid?
2. What is the difference between the area of a triangle and a parallelogram?
3. How do you find the height of a parallelogram if only the area and base are given?
4. Why is the area of a triangle \(\frac{1}{2} \times \text{base} \times \text{height}\)?
5. How can you use trigonometry to find unknown lengths in a right triangle?

**Tip**: In geometry, always ensure you understand the shapes and their respective formulas, as it helps simplify problems like these efficiently!

What is the area of the shaded part in the parallelogram?

Learn how to calculate the area of the shaded region in a parallelogram. This problem involves key geometric concepts such as the area of a parallelogram and a triangle, making it suitable for students in Grades 6-8.

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