Starting from the given formula:
[tex]A=\frac{h}{2}(a+b)[/tex]Multiply both sides of the equation by 2:
[tex]\begin{gathered} \Rightarrow2\times A=2\times\frac{h}{2}(a+b) \\ \Rightarrow2A=h(a+b) \end{gathered}[/tex]Divide both sides by h:
[tex]\begin{gathered} \Rightarrow\frac{2A}{h}=\frac{h(a+b)}{h} \\ \Rightarrow\frac{2A}{h}=a+b \end{gathered}[/tex]Substract a from both sides of the equation:
[tex]\begin{gathered} \Rightarrow\frac{2A}{h}-a=a+b-a \\ \Rightarrow\frac{2A}{h}-a=b \end{gathered}[/tex]Therefore:
[tex]b=\frac{2A}{h}-a[/tex]