Calculate Trapezoid Area: Find Area with Parallel Sides 6 and 12

What is the area of the trapezoid in the figure?

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

• Step 1: Identify the given information relevant to the trapezoid.
• 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: The problem gives us two bases, $b_1 = 6$ cm and $b_2 = 12$ cm, and a height $h = 4$ cm.
Step 2: We'll use the formula for the area of a trapezoid: $A = \frac{1}{2} \cdot (b_1 + b_2) \cdot h$
Step 3: Substituting in the given values: $A = \frac{1}{2} \cdot (6 + 12) \cdot 4 = \frac{1}{2} \cdot 18 \cdot 4 = \frac{72}{2} = 36 \text{ cm}^2$

Therefore, the solution to the problem is $36$ cm².