The given composite figure appears to be a combination of a rectangle and a right triangle.

1. Step 1: Split the composite shape

   • The main rectangle has dimensions of $10 \, \text{m}$ (length) and $5 \, \text{m}$ (height).
   • There is a right triangle on the right side with one leg of $4 \, \text{m}$ (height) and the base of $2 \, \text{m}$ (since the total length of the rectangle is $10 \, \text{m}$, and the total top length is $12 \, \text{m}$, making the difference $12 \, \text{m} - 10 \, \text{m} = 2 \, \text{m}$).

2. Step 2: Calculate the area of the rectangle $A_{\text{rectangle}} = \text{length} \times \text{height} = 10 \, \text{m} \times 5 \, \text{m} = 50 \, \text{m}^2$

3. Step 3: Calculate the area of the triangle The area of a right triangle is given by: $A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height}$ Here, the base is $2 \, \text{m}$ and the height is $4 \, \text{m}$: $A_{\text{triangle}} = \frac{1}{2} \times 2 \, \text{m} \times 4 \, \text{m} = 4 \, \text{m}^2$

4. Step 4: Total area of the composite figure To find the total area, add the areas of the rectangle and the triangle: $A_{\text{total}} = A_{\text{rectangle}} + A_{\text{triangle}} = 50 \, \text{m}^2 + 4 \, \text{m}^2 = 54 \, \text{m}^2$

Thus, the area of the composite figure is 54 square meters.

Would you like further details or have any questions about this?
Here are 5 related questions to expand on this concept:

1. How do you find the area of other composite figures with more complex shapes?
2. What is the importance of dividing composite figures into simpler shapes?
3. Can you calculate the perimeter of this composite figure?
4. How do you calculate the area of a trapezoid if present in a composite figure?
5. What other methods can be used to check the accuracy of area calculations?

Tip: When dealing with composite shapes, always break them down into simpler geometric figures whose area you can easily compute!