Given the rectangle's dimensions are 6 inches (width) and 12 inches (length), we can calculate its area. However, for the triangle on top, we'll need the height to determine its area. Assuming you want to proceed with the calculation of the rectangle first:

### Step-by-step Calculation:

1. **Area of the Rectangle:**
   - Length (\(l\)) = 12 inches
   - Width (\(w\)) = 6 inches

   The area (\(A_{\text{rect}}\)) of the rectangle is:
   \[
   A_{\text{rect}} = l \times w = 12 \times 6 = 72 \, \text{square inches}
   \]

2. **Area of the Triangle on Top:**
   - The base of the triangle is the same as the length of the rectangle, which is 12 inches.
   - To find the area of the triangle, we need its height (\(h\)). If you provide the height of the triangle, we can compute it using:
   \[
   A_{\text{tri}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 12 \times h = 6h \, \text{square inches}
   \]

3. **Total Area of the Figure:**
   - The total area of the figure combining the rectangle and triangle is:
   \[
   A_{\text{total}} = A_{\text{rect}} + A_{\text{tri}} = 72 + 6h \, \text{square inches}
   \]

### Conclusion:
The total area depends on the height of the triangle on top. If you provide the height, we can calculate the exact total area.

Would you like to provide the height of the triangle or need more details on this calculation?

### Related Questions:
1. How do you find the area if the triangle's height is 8 inches?
2. What is the perimeter of the composite figure?
3. How does the area change if the rectangle's dimensions are doubled?
4. How do you calculate the area of a triangle when the base and height are given?
5. What is the difference in area if the triangle on top is replaced with a semicircle?

**Tip:** When solving geometry problems, always sketch the figure to visualize the problem better and ensure the correct use of formulas.

Learn how to calculate the area of a rectangle with dimensions 6 inches by 12 inches, including the area of a triangle on top. Understand step-by-step calculations and formulas used in geometry. Suitable for students in Grades 6-8.

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