#### Answer

$h=\dfrac{2A}{a+b}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
A=\dfrac{1}{2}ah+\dfrac{1}{2}bh
$ for $
h
,$ use the properties of equality to isolate the variable.
$\bf{\text{Solution Details:}}$
Using the properties of equality to isolate the variable, the equation above is equivalent to
\begin{array}{l}\require{cancel}
A=\dfrac{1}{2}ah+\dfrac{1}{2}bh
\\\\
2(A)=2\left( \dfrac{1}{2}ah+\dfrac{1}{2}bh \right)
\\\\
2A=ah+bh
\\\\
2A=h(a+b)
\\\\
\dfrac{2A}{a+b}=\dfrac{h(a+b)}{a+b}
\\\\
\dfrac{2A}{a+b}=h
\\\\
h=\dfrac{2A}{a+b}
.\end{array}