The diagram shows a quadrilateral, PQRS - OCR - GCSE Maths - Question 11 - 2023 - Paper 6

The area of a trapezoid can be calculated using the formula:

$$Area = \frac{(b_1 + b_2) \times h}{2}$$

Here, b1 = PQ = x cm, b2 = SR = x + 6 cm, and h = 10 cm.

Thus, we have:

$$A = \frac{(x + (x + 6)) \times 10}{2}$$

Simplifying this gives:

$$A = \frac{(2x + 6) \times 10}{2} = (2x + 6) \times 5 = 10x + 30$$

Rearranging the area equation:

$$10x + 30 = A$$

Then, isolate x:

$$10x = A - 30$$

And finally, divide by 10:

$$PQ = x = \frac{A - 30}{10}$$

Thus, we have the expression for PQ in terms of A as:

$$PQ = \frac{A - 30}{10}$$