Trapezium Cut in Half By Line Parallel to Slant Height

A trapezium ABCD with parallel sides 10 and 4, and height 8 is to be cut in half parallel to a slanted side.

The result is a trapezium and a parallelogram. If the base of the parallelogram is  
  then the base of the smaller trapezium is  
  and the top side has length  

The area of the small trapezium is  
\[\frac{1}{2}(10-x+4-x) \times 8=56-8x\]
  and the area of the parallelogram is  
Equating these gives  
\[56-8x=8x \rightarrow 16x=56 \rightarrow x= \frac{56}{16}=3.5\]

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