Set up the area equation

Using the area formula for a trapezium, substitute the given height $h = 52$ and Area $A = 988$.

$988 = \frac{1}{2} \times (a + b) \times 52$

Calculate the sum of parallel sides

Simplify the equation to find $(a + b)$. Dividing 988 by 26 gives the sum.

$a + b = \frac{988 \times 2}{52} = 38$

Solve the system of linear equations

We have two equations: $a + b = 38$ and $a - b = 9$. Adding them gives $2a = 47$, so $a = 23.5$.

$a = \frac{47}{2} = 23.5$

Find the second side

Substitute $a = 23.5$ into $a + b = 38$ to find $b$.

$b = 38 - 23.5 = 14.5$