## 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
$x$
then the base of the smaller trapezium is
$10-x$
and the top side has length
$4-x$
.

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
$8x$
.
Equating these gives
$56-8x=8x \rightarrow 16x=56 \rightarrow x= \frac{56}{16}=3.5$