To find the total area of the window, we need to calculate the area of each trapezoid and then sum their areas.
The area \( A \) of a trapezoid can be calculated using the formula:
\[ A = \frac{1}{2} \times (b_1 + b_2) \times h \]
where \( b_1 \) and \( b_2 \) are the lengths of the two bases, and \( h \) is the height.
Area of the Top Trapezoid
For the top trapezoid:
- Top base \( b_1 = 16 \) inches
- Bottom base \( b_2 = 30 \) inches
- Height \( h = 12 \) inches
Substituting the values into the formula:
\[ A_{top} = \frac{1}{2} \times (16 + 30) \times 12 \]
Calculating \( (16 + 30) \):
\[ 16 + 30 = 46 \]
Now substituting back into the area formula:
\[ A_{top} = \frac{1}{2} \times 46 \times 12 \]
Calculating \( \frac{1}{2} \times 46 \):
\[ \frac{1}{2} \times 46 = 23 \]
Now calculating the complete area of the top trapezoid:
\[ A_{top} = 23 \times 12 = 276 \text{ in}^2 \]
Area of the Bottom Trapezoid
For the bottom trapezoid:
- Top base \( b_1 = 30 \) inches
- Bottom base \( b_2 = 16 \) inches
- Height \( h \) is not given explicitly, but since the bottom trapezoid also has a right leg of 20 inches, we will use that to calculate the height using the property of trapezoids if needed.
However, as per the problem description, it implies symmetry in dimensions, hence we assume that the height of the bottom trapezoid is also equal to \( h = 12 \) inches.
Using the same values as for the top trapezoid but switching the bases:
\[ A_{bottom} = \frac{1}{2} \times (30 + 16) \times 12 \]
Calculating \( (30 + 16) \):
\[ 30 + 16 = 46 \]
Substituting back into the area formula:
\[ A_{bottom} = \frac{1}{2} \times 46 \times 12 \]
Following the same steps as above:
\[ A_{bottom} = 23 \times 12 = 276 \text{ in}^2 \]
Total Area of the Window
Finally, we add the areas of both trapezoids to find the total area:
\[ A_{total} = A_{top} + A_{bottom} = 276 + 276 \]
Calculating gives:
\[ A_{total} = 552 \text{ in}^2 \]
Thus, the total area of the window in square inches is:
\[ \boxed{552} \text{ in}^2 \]