What is the area of this figure?

Enter your answer in the box.

 
 m²

A parallelogram with a right triangle created inside it with a short leg length of 5 m and a long leg length of 9 m. Two triangles attached to the top of the parallelogram are touching and share a long leg length of 8 m.

To find the area of the given figure, we must calculate the area of the parallelogram and adjust it by accounting for the additional and subtracted triangular areas.

### Step 1: Identify Key Shapes
1. **Parallelogram**:
   - A parallelogram's area is \( A_{\text{parallelogram}} = \text{base} \times \text{height} \).  
   - Here, the parallelogram's base is \( 9 \, \text{m} \) (long leg of the triangle), and the height is \( 5 \, \text{m} \) (short leg of the triangle).
   - Therefore:
     \[
     A_{\text{parallelogram}} = 9 \times 5 = 45 \, \text{m}^2.
     \]

2. **Additional Triangles**:
   - Two triangles with base \( 8 \, \text{m} \) and shared height \( 5 \, \text{m} \) are attached to the top of the parallelogram.
   - The area of one triangle is:
     \[
     A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8 \times 5 = 20 \, \text{m}^2.
     \]
   - Since there are two such triangles, their total area is:
     \[
     A_{\text{added triangles}} = 2 \times 20 = 40 \, \text{m}^2.
     \]

3. **Subtracted Triangle**:
   - Inside the parallelogram is a right triangle with base \( 9 \, \text{m} \) and height \( 5 \, \text{m} \).
   - Its area is:
     \[
     A_{\text{subtracted triangle}} = \frac{1}{2} \times 9 \times 5 = 22.5 \, \text{m}^2.
     \]

### Step 2: Calculate the Total Area
Combine the areas:
\[
A_{\text{total}} = A_{\text{parallelogram}} + A_{\text{added triangles}} - A_{\text{subtracted triangle}}.
\]
Substituting the values:
\[
A_{\text{total}} = 45 + 40 - 22.5 = 62.5 \, \text{m}^2.
\]

### Final Answer:
The area of the figure is:
\[
\boxed{62.5 \, \text{m}^2}.
\]

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Would you like more details or have any questions?  

Here are 5 related questions to deepen your understanding:  
1. How do you calculate the area of a parallelogram in general?  
2. Why is the formula for a triangle's area \( \frac{1}{2} \times \text{base} \times \text{height} \)?  
3. How would the area change if the attached triangles had different heights?  
4. What happens to the area of the parallelogram if one side is doubled?  
5. Can you determine the perimeter of the entire figure using the given dimensions?  

**Tip**: When solving composite figure problems, always separate and analyze the individual shapes to avoid confusion!

What is the area of this figure? Enter your answer in the box. A parallelogram with a right triangle created inside it with a short leg length of 5 m and a long leg length of 9 m. Two triangles attached to the top of the parallelogram are touching and share a long leg length of 8 m.

Learn how to calculate the area of a composite figure containing a parallelogram and triangles. This step-by-step solution uses geometry concepts and formulas for areas of parallelograms and triangles. Ideal for students in Grades 6-8.

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