In a trapezoid with a certain height, and two parallel sides,
it does not matter which way the non-parallel sides slant,
or whether one of them is vertical.  We know the other base is
longer than 6 because if it were 6 the area would only be 6x18
or 108.  So let's draw the trapezoid with the unknown parallel
side longer that the given one and one of the non-parallel
side vertical:




Now we'll draw in a (green) altitude to show that the area is
just the area of a rectangle plus the area of a triangle.



Area of rectangle + Area of triangle = Area of trapezoid:

         

         108 + 9x = 162
               9x = 54
                x = 6

So the other (bottom) base of the trapezoid = 6+x = 6+6 = 12

Answer:  12 cm

Edwin

The other way to do this problem is to memorize the formula for
the area of a trapezoid:



where capital B is one parallel side and small b is the other parallel side
and h is the height:

So we substitute A=162, b=6, h=18 and leave the B unknown to solve for:


  
   
    
     

Edwin