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Chapter 0: Problem 31

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

Short Answer

Expert verified
The formula for \(a\) based on the given equation is \(a = \frac{2A}{h} - b\).

Step by step solution

01

Understand the equation structure

The starting equation is \(A = \frac{1}{2} h(a + b)\). It is known that \(A\) represents the area of a trapezoid, \(h\) represents the height and \(a\) and \(b\) are the lengths of both parallel sides.
02

Remove the fraction by multiplying entire equation by 2

To remove the fraction \(\frac{1}{2}\), multiply the entire equation by 2. The equation now becomes \(2A = h(a + b)\).
03

Isolate the variable a

To isolate \(a\), first, divide both sides of the equation by \(h\). This yields \( \frac{2A}{h} = a + b \). Finally, to get \(a\) alone, subtract \(b\) from both sides. The result is the formula \(a = \frac{2A}{h} - b\). Now, the formula is solved specifically for \(a\).

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