The area of a trapezoid can be calculated with this formula:
[tex]A=\frac{h(B+b)}{2}[/tex]Where "A" is the area, "h" is the height, and "B" and "b" are the bases.
In this case, you can identify that:
[tex]\begin{gathered} A=\frac{17}{420}cm^2 \\ \\ B=\frac{2}{7}cm \\ \\ b=\frac{1}{5}cm \end{gathered}[/tex]Then you can substitute these values into the formula and solve for "h". This is:
[tex]\begin{gathered} \frac{17}{420}^{}=\frac{h(\frac{2}{7}+\frac{1}{5})}{2} \\ \\ (2)(\frac{17}{420})=h(\frac{2}{7}+\frac{1}{5}) \\ \\ \frac{17}{210}=h(\frac{17}{35}) \\ \\ (\frac{17}{210})(\frac{35}{17})=h \\ \\ h=\frac{1}{6}cm \\ \\ h\approx0.2\operatorname{cm} \end{gathered}[/tex]The answer is:
[tex]h\approx0.2\operatorname{cm}[/tex]