Problem 66 - College Algebra Essentials

Question

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? $$A=\frac{1}{2} h(a+b) \text { for } b$$

Step-by-Step Solution

Answer

The solution to \( b \) in the given trapezoid formula is \( \frac{2A}{h} - a \).

Step 1: Understand the Formula

The given formula is used for finding the area of a trapezoid: \(A= \frac{1}{2}h(a+b)\). In this formula, A stands for area, h is the height of the trapezoid, and a and b are the lengths of the two bases. The goal is to solve for b.

Step 2: Isolate the Expression with b

We start by isolating the 'a + b' part by multiplying the entire equation by \( \frac{2}{h}\). This gives us \( \frac{2A}{h} = a+b \).

Step 3: Solve for b

Now, we subtract a from both sides to get b alone: \( \frac{2A}{h}-a = b \).