To find the area of the figure composed of two trapezoids, we can break it down into two individual trapezoids and calculate their areas separately.
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Top trapezoid:
- Top base (length) = 8 cm
- Bottom base (length) = 6 cm
- Height (length of the sides) = 5 cm (since both sides are equal)
The formula for the area \( A \) of a trapezoid is:
\[ A = \frac{1}{2} \times (b_1 + b_2) \times h \]
where \( b_1 \) and \( b_2 \) are the lengths of the two bases, and \( h \) is the height.
Plugging in the values for the top trapezoid:
\[ A_{top} = \frac{1}{2} \times (8 , \text{cm} + 6 , \text{cm}) \times 5 , \text{cm } = \frac{1}{2} \times 14 , \text{cm} \times 5 , \text{cm} = \frac{70}{2} = 35 , \text{cm}^2 \]
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Bottom trapezoid:
- Top base (length) = 6 cm (this is the bottom of the top trapezoid which is the top base of the bottom trapezoid)
- Bottom base (length) = 9 cm
- Height = 5 cm
Using the trapezoid area formula again:
\[ A_{bottom} = \frac{1}{2} \times (6 , \text{cm} + 9 , \text{cm}) \times 5 , \text{cm} \]
Simplifying:
\[ A_{bottom} = \frac{1}{2} \times 15 , \text{cm} \times 5 , \text{cm} = \frac{75}{2} = 37.5 , \text{cm}^2 \]
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Total area of the figure: Now, we combine the areas of both trapezoids:
\[ A_{total} = A_{top} + A_{bottom} = 35 , \text{cm}^2 + 37.5 , \text{cm}^2 = 72.5 , \text{cm}^2 \]
Thus, the area of the figure is \( \boxed{72.5} \) square centimeters.