To calculate the total area of the desk, we need to find the area of each trapezoid separately and then sum the two areas.
The formula for the area \( A \) of a trapezoid is given by:
\[ A = \frac{1}{2} \times (b_1 + b_2) \times h \]
where:
- \( b_1 \) is the length of the top base,
- \( b_2 \) is the length of the bottom base, and
- \( h \) is the height of the trapezoid.
Area of Trapezoid A
For trapezoid A:
- \( b_1 = 5 \) feet (top base)
- \( b_2 = 8 \) feet (bottom base)
- \( h = 3 \) feet (height)
Substituting these values into the formula:
\[ A_A = \frac{1}{2} \times (5 + 8) \times 3 \] \[ A_A = \frac{1}{2} \times 13 \times 3 \] \[ A_A = \frac{1}{2} \times 39 \] \[ A_A = 19.5 \text{ ft}^2 \]
Area of Trapezoid B
For trapezoid B:
- \( b_1 = 4 \) feet (top base)
- \( b_2 = 9 \) feet (bottom base)
- \( h = 3 \) feet (height)
Substituting these values into the formula:
\[ A_B = \frac{1}{2} \times (4 + 9) \times 3 \] \[ A_B = \frac{1}{2} \times 13 \times 3 \] \[ A_B = \frac{1}{2} \times 39 \] \[ A_B = 19.5 \text{ ft}^2 \]
Total Area of the Desk
Now, we add the areas of trapezoid A and trapezoid B to find the total area of the desk:
\[ A_{\text{total}} = A_A + A_B \] \[ A_{\text{total}} = 19.5 + 19.5 \] \[ A_{\text{total}} = 39 \text{ ft}^2 \]
Thus, the total area of the desk is
\(\boxed{39}\) ft².