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# Towering Trapeziums

##### Age 14 to 16Challenge Level

$OGH$ is an isosceles right-angled triangle: Lines $AB$, $CD$, $EF$, and $GH$ are parallel.

Suppose the area of the smallest triangle $OAB$ is one square unit.
• If lines $OC$ and $AB$ have the same length, calculate the area of trapezium $ABDC$.
• If lines $OE$ and $CD$ also have the same length, calculate the area of trapezium $CDFE$.
• If lines $OG$ and $EF$ also have the same length, calculate the area of trapezium $EFHG$.
Suppose that the chain of trapezia continued.

What would be the area of the $n^{th}$ trapezium in the chain?