#### Answer

$20\ cm^2$

#### Work Step by Step

If the height is $h$, the base is $3h-7$.
Write an equation to find the height.
$b=3h-7$
$5=3h-7\longrightarrow$ substitute the given base size
$12=3h\longrightarrow$ addition property of equality
$4=h\longrightarrow$ division property of equality
$A=bh=5\times4=20$