We can draw the trapezoid as follows
Recall that the area of a trapezoid of the shape
Is given by the formula

In our case, we have b=1/5, B = 2/7 and the area is 17/420. So we have the following equation

so we need to solve this equation for h.
We start by solving this operation

Recall that given two fractions a/b and c/d we have

Taking a=2, b=7, c=1 and d=5, we get

So we have the equation

Now, recall that givens numbers a,b,c where b and c are not zero, we have that

In our case, lets take a=17, b=35 and c=2. So we have

So we have the equation

We can divide both sides by 17, so we get

So if we multiply both sides by 70, we get

So the height of the trapezoid is h=1/6 cm.