Answer
a) $b=\dfrac{2A-hB}{h}$
b) $B=\dfrac{2A-hb}{h}$
Work Step by Step
a) Using the properties of equality, in terms of $
b
,$ the given formula, $
A=\dfrac{1}{2}h(b+B)
,$ is equivalent to
\begin{array}{l}\require{cancel}
2A=h(b+B)
\\\\
2A=hb+hB
\\\\
2A-hB=hb
\\\\
\dfrac{2A-hB}{h}=b
\\\\
b=\dfrac{2A-hB}{h}
.\end{array}
b) Using the properties of equality, in terms of $
B
,$ the given formula, $
A=\dfrac{1}{2}h(b+B)
,$ is equivalent to
\begin{array}{l}\require{cancel}
2A=h(b+B)
\\\\
2A=hb+hB
\\\\
2A-hb=hB
\\\\
\dfrac{2A-hb}{h}=B
\\\\
B=\dfrac{2A-hb}{h}
.\end{array}
