In a trapezium the two parallel sides are 25 cm and 10 cm, and the two non-parallel (slant) sides are 14 cm and 13 cm. Find the area of the trapezium in ${\text{cm}}^2$.

Drop a perpendicular from each end of the shorter parallel side. The two horizontal pieces $x$ and $y$ satisfy $x+y=25-10=15$, and the common height gives $14^2-x^2=13^2-y^2$, i.e. $y^2-x^2=-27$. So $(y-x)(15)=-27,y-x=-1.8$, giving $x=8.4$ and $y=6.6$. Height = √(196 − 70.56) = √125.44 = 11.2 cm. Area = ½ × $(25+10)\times 11.2$ = ½ × $35\times 11.2=196{\text{cm}}^2$.