In a trapezium the segment joining the midpoints of the two slanting sides is 18 cm long, and the distance between the two parallel sides is 7 cm. Find the area of the trapezium in ${\text{cm}}^2$.

The segment joining the midpoints of the slanting sides equals HALF the sum of the parallel sides, so $a+b=36$ cm. Area = ½$(a+b)h$ = ½ × $36\times 7=126{\text{cm}}^2$ — that is simply $18\times 7$, the midline times the height. (Halving a second time gives $63{\text{cm}}^2$; $252{\text{cm}}^2$ uses $36\times 7$ and forgets the ½; $25{\text{cm}}^2$ adds 18 and 7 instead of multiplying.)