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The area of a trapezoid is given by the formula A = (a + b). Solve the formula for b.

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Starting from the given formula:


A=(h)/(2)(a+b)

Multiply both sides of the equation by 2:


\begin{gathered} \Rightarrow2* A=2*(h)/(2)(a+b) \\ \Rightarrow2A=h(a+b) \end{gathered}

Divide both sides by h:


\begin{gathered} \Rightarrow(2A)/(h)=(h(a+b))/(h) \\ \Rightarrow(2A)/(h)=a+b \end{gathered}

Substract a from both sides of the equation:


\begin{gathered} \Rightarrow(2A)/(h)-a=a+b-a \\ \Rightarrow(2A)/(h)-a=b \end{gathered}

Therefore:


b=(2A)/(h)-a

User Shaig Khaligli
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