Question

The area of a trapezoid is given by the formula A = 1/2 (b 1 + b 2)h, where base b 1 is parallel to base b 2 and h is the height. Solve the formula for b 2. Show your work.

Answer 1

Answer:

$b_{2} = \frac{2A}{h} -b_{1}$

Step-by-step explanation:

Our aim is to solve the formula in terms of b.

We know that the formula of trapezoid's are is the following:

$A=\frac{1}{2}(b_{1}+b_{2})h$

In order to simplify it we can use distributive property, this means, [a(b+c)=ab+ac] and we get something like the following:

$A=\frac{1}{2}hb_{1}+\frac{1}{2}hb_{2}$

Thus, we need to solve it in terms of b, using calculus and solving the equation. Therefore:

$A-\frac{1}{2}hb_{1}=\frac{1}{2}hb_{2}\\\frac{A-\frac{1}{2}hb_{1}}{\frac{1}{2}h}=b_{2}\\\frac{A}{\frac{h}{2}}-\frac{\frac{1}{2}hb_{1}}{\frac{1}{2}h}=b_{2}\\\frac{2A}{h}-b_{1}=b_{2}$

Hence $b_{2} = \frac{2A}{h} -b_{1}$

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