Let's break down the problem step by step based on the image provided. The shape is a trapezium $PQRS$, with $PQ \parallel RS$ and $\angle PSR = 90^\circ$. We are given the following dimensions:

• $PQ = x$ cm (parallel side),
• $PS = (x + 3)$ cm (height),
• $RS = (3x - 2)$ cm (parallel side).

We are asked to:

(a) Form an equation in $x$ for the area of the trapezium and simplify it.

The formula for the area $A$ of a trapezium is:

$A = \frac{1}{2} \times \text{sum of parallel sides} \times \text{height}$

Here, the parallel sides are $PQ = x$ and $RS = (3x - 2)$, and the height is $PS = (x + 3)$. The area is given as 49 cm². So, substituting into the formula:

[ 49 = \frac{1}{2} \times (x + (3x - 2)) \times (x +