Question 1202022
<br>
Here is a crude sketch based on the given information:<br><pre>

                   26
        ************************
       *                         *
      *                            *
     *   A = 618                     *
    *                                  *
   *************************************** -----------
  *                                        *
 *      A = 636                              * height x
************************************************-----
                    50
</pre>
The area of the trapezoid is 1254, which is (altitude) times (average of bases):<br>
1254 = h((50+26)/2)
1254 = 38h
h = 1254/38 = 33<br>
Since the height of the lower portion is x, the height of the upper portion is 33-x.<br>
Since the formula for the area of a trapezoid is (altitude) times (average of bases), for convenience let 2y be the length of the segment parallel to the two bases.  We then have this sketch:<br><pre>

                   26
        ************************----------------------
       *                         *
      *                            *
     *   A = 618                     *    height 33-x
    *                 2y               *
   *************************************** -----------
  *                                        *
 *      A = 636                              * height x
************************************************-----
                    50
</pre>
Then for the areas of the two trapezoids we have<br>
{{{(33-x)((2y+26)/2)=618}}} [1]
{{{x((2y+50)/2)=636}}} [2]<br>
Simplify [1]<br>
{{{(33-x)(y+13)=618}}}
{{{33y+429-xy-13x=618}}}
{{{-xy-13x+33y=189}}} [3]<br>
Simplify [2]<br>
{{{x(y+25)=636}}}
{{{xy+25x=636}}} [4]<br>
Add [3] and [4]<br>
{{{12x+33y=825}}}
{{{4x+11y=275}}} [5]<br>
Solve [5] for x and substitute in [4]<br>
I leave the rest to you.  The numbers work out to give a very ugly irrational value for x, which leads me to believe that the given numbers are not right....<br>