Trapezoid Area Problem: Finding AB When Area = 77 and Height = 7

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

• Step 1: Identify the given information
• Step 2: Apply the formula for the area of a trapezoid
• Step 3: Solve for the unknown side $AB$

Now, let's work through each step:
Step 1: The problem gives us the height $h = 7$, the base $CD = 12$, and the area $A = 77$. We need to find the length of $AB$.
Step 2: We'll use the formula for the area of a trapezoid: $A = \frac{1}{2} (b_1 + b_2) \times h$ which gives us: $77 = \frac{1}{2} (AB + 12) \times 7$
Step 3: Simplifying the equation: $77 = \frac{7}{2} (AB + 12)$ Multiply both sides by 2 to clear the fraction: $154 = 7 (AB + 12)$ Divide both sides by 7: $22 = AB + 12$ Subtract 12 from both sides to solve for $AB$: $AB = 10$

Therefore, the solution to the problem is $AB = 10$.