The formula for a trapezoid relates the area A, the two bases, a and b, and the height, h.

A=h(a+b)/2

Solve for b.

To solve for \( b \) in the trapezoid area formula:

\[
A = \frac{h(a + b)}{2}
\]

Follow these steps:

1. Multiply both sides of the equation by 2 to eliminate the denominator:
   \[
   2A = h(a + b)
   \]

2. Divide both sides by \( h \) to isolate \( (a + b) \):
   \[
   \frac{2A}{h} = a + b
   \]

3. Subtract \( a \) from both sides to solve for \( b \):
   \[
   b = \frac{2A}{h} - a
   \]

Thus, the expression for \( b \) is:
\[
b = \frac{2A}{h} - a
\]

Would you like more details on any part of this process?

Here are five related questions to consider:
1. What happens if the height \( h \) is doubled in the formula?
2. How does changing one of the bases affect the area?
3. Can you derive the formula for the height \( h \) in terms of \( A \), \( a \), and \( b \)?
4. How does this formula apply when the trapezoid is isosceles?
5. What are some real-world applications of trapezoid area calculations?

**Tip:** Always make sure to simplify the equation step by step to avoid mistakes when rearranging formulas.

The formula for a trapezoid relates the area A, the two bases, a and b, and the height, h. A=h(a+b)/2. Solve for b.

Learn how to solve for base b in the trapezoid area formula A = h(a + b)/2. This detailed solution covers key algebraic concepts and step-by-step rearrangement of the formula, suitable for students in Grades 8-10.

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