Consider that the area of a trapezium is given by,
[tex]\text{Area}=\frac{1}{2}\times(\text{sum of parallel sides)}\times\text{ height}[/tex]According to the given problem,
[tex]\begin{gathered} \text{Area}=\frac{17}{420} \\ \text{Parallel sides=}\frac{2}{7},\text{ }\frac{1}{5} \end{gathered}[/tex]Substitute the values and solve for the height as,
[tex]\begin{gathered} \frac{17}{420}=\frac{1}{2}\times(\frac{2}{7}+\frac{1}{5})\times h \\ \frac{17}{210}=(\frac{17}{35})\times h \\ h=\frac{35}{210} \\ h=\frac{1}{6} \\ h\approx0.2 \end{gathered}[/tex]Thus, the height of the trapezium is 0.2 cm approximately.
