The diagram shows rectangle STUV - Edexcel - GCSE Maths - Question 8 - 2022 - Paper 3

The area of triangle TQU can be calculated as follows:

$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

Here, the base is 2x cm and the height is 4 cm. Thus,

$\text{Area} = \frac{1}{2} \times 2x \times 4 = 4x.$

To calculate the area of trapezium QUVR, we use the formula:

$A = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{height}$

Here, Base_1 = 5 cm (length QU) and Base_2 = 3 cm (length RV), with the height being 4 cm. Thus,

$A = \frac{1}{2} \times (5 + 3) \times 4 = 16.$

Finally, combining the areas from the rectangle and triangle gives:

$A = 20x - 4x = 16.$

We conclude that:

$A = 2x^2 + 20x.$