Question: Solve the equation for the indicated variable.
A = \frac{b_1 + b_2}{2} h ; h
h =
(Simplify your answer. Use integers or fractions for any numbers in the expression.)
1. **State the problem:** We are given the formula for the area of a trapezoid:
$$A = \frac{(b_1 + b_2)h}{2}$$
and we need to solve for the variable $h$.
2. **Write the formula and isolate $h$:**
Start with:
$$A = \frac{(b_1 + b_2)h}{2}$$
To isolate $h$, multiply both sides by 2 to get rid of the denominator:
$$2A = (b_1 + b_2)h$$
3. **Divide both sides by $(b_1 + b_2)$ to solve for $h$:**
$$h = \frac{2A}{b_1 + b_2}$$
4. **Show the cancellation step explicitly:**
$$h = \frac{\cancel{2}A}{\cancel{b_1 + b_2}} \times \frac{2}{b_1 + b_2} = \frac{2A}{b_1 + b_2}$$
(Note: Here the cancellation is symbolic to show division by the entire sum $b_1 + b_2$.)
5. **Final answer:**
$$\boxed{h = \frac{2A}{b_1 + b_2}}$$
This formula expresses $h$ in terms of $A$, $b_1$, and $b_2$.