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Chapter 6: Problem 54

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

Short Answer

Expert verified
The solution to the formula for \(b\) is \(b = \frac{2A}{h} - a\).

Step by step solution

01

Identify the formula

The formula \(A=\frac{1}{2} h(a+b)\) is used to calculate the area of a trapezoid. Where \(A\) is the area, \(h\) is the height, and \(a\), \(b\) are the lengths of the 2 parallel sides.
02

Rearrange the formula to isolate h(a+b)

Multiplying both sides of the equation by 2 in order to isolate \(h(a + b)\) results in \(2A = h(a + b)\).
03

Isolate (a+b)

To isolate \(a + b\), divide both sides of the equation by \(h\). The equation becomes \(\frac{2A}{h} = a + b\).
04

Solve for b

Finally, to solve for \(b\), subtract \(a\) from both sides of the equation. The final equation is \(b = \frac{2A}{h} - a\).

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