To find the area of the composite shape made up of the two trapezoids, we'll calculate the area of each trapezoid separately using the formula for the area of a trapezoid:
\[ \text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h \]
where \(b_1\) and \(b_2\) are the lengths of the two bases, and \(h\) is the height.
Top Trapezoid:
- Bases: \(b_1 = 8\) cm and \(b_2 = 6\) cm
- Height: \(h = 5\) cm
Calculating the area:
\[ \text{Area}_{\text{top}} = \frac{1}{2} \times (8 + 6) \times 5 \] \[ = \frac{1}{2} \times 14 \times 5 \] \[ = 7 \times 5 = 35 \text{ cm}^2 \]
Bottom Trapezoid:
- Bases: \(b_1 = 6\) cm and \(b_2 = 9\) cm
- Height: \(h = 5\) cm
Calculating the area:
\[ \text{Area}_{\text{bottom}} = \frac{1}{2} \times (6 + 9) \times 5 \] \[ = \frac{1}{2} \times 15 \times 5 \] \[ = 7.5 \times 5 = 37.5 \text{ cm}^2 \]
Total Area: Now, we add the areas of both trapezoids:
\[ \text{Total Area} = \text{Area}{\text{top}} + \text{Area}{\text{bottom}} \] \[ = 35 + 37.5 = 72.5 \text{ cm}^2 \]
Thus, the total area of the figure is \(72.5 \text{ cm}^2\).
The highlighted answer option \(72.5 \text{ cm}^2\) is correct.