We can draw the trapezoid as follows
Recall that the area of a trapezoid of the shape
Is given by the formula
[tex]\frac{(B+b)\cdot h}{2}[/tex]In our case, we have b=1/5, B = 2/7 and the area is 17/420. So we have the following equation
[tex]\frac{17}{420}=\frac{(\frac{2}{7}+\frac{1}{5})\cdot h}{2}[/tex]so we need to solve this equation for h.
We start by solving this operation
[tex]\frac{2}{7}+\frac{1}{5}[/tex]Recall that given two fractions a/b and c/d we have
[tex]\frac{a}{b}+\frac{c}{d}=\frac{a\cdot d+c\cdot b}{b\cdot d}[/tex]Taking a=2, b=7, c=1 and d=5, we get
[tex]\frac{2}{7}+\frac{1}{5}=\frac{2\cdot5+1\cdot7}{7\cdot5}=\frac{17}{35}[/tex]So we have the equation
[tex]\frac{17}{420}=\frac{\frac{17}{35}\cdot h}{2}[/tex]Now, recall that givens numbers a,b,c where b and c are not zero, we have that
[tex]\frac{\frac{a}{b}}{c}=\frac{a}{b\cdot c}[/tex]In our case, lets take a=17, b=35 and c=2. So we have
[tex]\frac{\frac{17}{35}}{2}=\frac{17}{35\cdot2}=\frac{17}{70}[/tex]So we have the equation
[tex]\frac{17}{420}=\frac{17}{70}\cdot h[/tex]We can divide both sides by 17, so we get
[tex]\frac{1}{420}=\frac{h}{70}[/tex]So if we multiply both sides by 70, we get
[tex]h=\frac{70}{420}=\frac{7}{42}=\frac{1}{6}[/tex]So the height of the trapezoid is h=1/6 cm.
