The area of a trapezoid is given by:
Where:
• h is the heigh,
,
• a and b are the length of the parallel sides.
In this problem, we have:
• A = 180 cm²,
,
• h = 18 cm,
• a = 5 cm,
,
• b = x.
Replacing these data in the equation above, we have:
![180cm^2=(1)/(2)\cdot18\operatorname{cm}\cdot(5\operatorname{cm}+x)\text{.}]()
Solving for x the last equation, we get:
![\begin{gathered} \frac{2\cdot180cm^2}{18\operatorname{cm}}=5\operatorname{cm}+x, \\ 20\operatorname{cm}=5\operatorname{cm}+x, \\ x=20\operatorname{cm}-5\operatorname{cm}, \\ x=15\operatorname{cm}\text{.} \end{gathered}]()
So the length of the second parallel side is:
![x=15\operatorname{cm}\text{.}]()
Answer: 15 cm