https://file.aiquickdraw.com/mathbot/file/172540340326724m8w3bp.jpg

The given formula in the image is:

\[
A = \frac{1}{2} h (b_1 + b_2)
\]

This is the formula for the area \(A\) of a trapezoid, where \(h\) is the height, \(b_1\) is the length of the first base, and \(b_2\) is the length of the second base.

To solve for \(b_2\), we need to isolate \(b_2\) on one side of the equation:

1. Start with the formula:
   \[
   A = \frac{1}{2} h (b_1 + b_2)
   \]

2. Multiply both sides by 2 to get rid of the fraction:
   \[
   2A = h (b_1 + b_2)
   \]

3. Divide both sides by \(h\) to isolate the term \((b_1 + b_2)\):
   \[
   \frac{2A}{h} = b_1 + b_2
   \]

4. Subtract \(b_1\) from both sides to solve for \(b_2\):
   \[
   b_2 = \frac{2A}{h} - b_1
   \]

Thus, the length of the second base \(b_2\) can be calculated using the formula:

\[
b_2 = \frac{2A}{h} - b_1
\]

Would you like to go into further details or have any questions?

### 5 Relative Questions:
1. How would you solve for \(h\) given the same formula?
2. How do you derive the formula for the area of a trapezoid?
3. What are the implications if \(b_1 = b_2\) in the trapezoid area formula?
4. How can you apply this formula in real-world problems involving trapezoids?
5. What happens if the height \(h\) approaches zero? How does it affect the area?

### Tip:
When solving equations, always aim to isolate the variable you want to solve for by using algebraic operations systematically.

Solve for b2 given the equation A = 1/2 * h * (b1 + b2).

Learn how to solve for the second base b2 in the trapezoid area formula A = 1/2 * h * (b1 + b2). This problem covers algebraic manipulation and basic geometry concepts, suitable for students in Grades 7-9.

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