Answer
$20$ cm
Work Step by Step
$A=0.5\cdot b\cdot h,$ and
b varies inversely as h $\Rightarrow b=\displaystyle \frac{k}{h}$, for some constant k.
We can write
$A=0.5\displaystyle \cdot\frac{k}{h}\cdot k=0.5k$
Given $b=8$ when $ h=10, $we find k
$8=\displaystyle \frac{k}{10}\quad\Rightarrow\quad k=80.$
$ A=0.5(80)=40.$
(Whatever the height, the area is $40 \mathrm{c}\mathrm{m}^{2})$
The base, when $h=4$ is
$b=\displaystyle \frac{80}{4}=20$ cm
