Calculate Trapezoid Area: ABCD with Bases 10cm, 7cm and Height 5cm

To solve this problem, we'll follow these steps:

• Step 1: Identify the given information.
• Step 2: Apply the appropriate formula for the area of a trapezoid.
• Step 3: Perform the necessary calculations to find the area.

Now, let's work through each step:

Step 1: We are given that the bases of the trapezoid $AB = 10 \, \text{cm}$ and $DC = 7 \, \text{cm}$, and the height of the trapezoid is $5 \, \text{cm}$.

Step 2: The formula for finding the area of a trapezoid is: $\text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}$

Step 3: Substituting the known values into the formula, we have: $\text{Area} = \frac{1}{2} \times (10 + 7) \times 5$

Simplifying inside the parentheses and calculating, we get: $\text{Area} = \frac{1}{2} \times 17 \times 5 = \frac{1}{2} \times 85 = 42.5$

Therefore, the area of trapezoid ABCD is $\textbf{42.5}$ square centimeters.

Thus, the correct choice from the provided options is 42.5.