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

Question 11

The diagram shows a quadrilateral, PQRS. PS = 10 cm. Angle QPS = Angle PSR = 90°. SR is 6 cm longer than PQ. The area of quadrilateral PQRS is A cm². Write a simpl... show full transcript

Worked Solution & Example Answer:The diagram shows a quadrilateral, PQRS - OCR - GCSE Maths - Question 11 - 2023 - Paper 6

Step 1

Calculate the expression for the area of PQRS

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Answer

Given that PQ = x, then SR = x + 6. The height PS is 10 cm. The area (A) of PQRS can be calculated using the formula for the area of a trapezoid:

$A = \frac{1}{2} \times (PQ + SR) \times PS$

Substituting the values we have:

$A = \frac{1}{2} \times (x + (x + 6)) \times 10$

Simplifying this, we find:

$A = \frac{1}{2} \times (2x + 6) \times 10 = (2x + 6) \times 5$

Thus,

$A = 10x + 30$

Step 2

Solve for PQ in terms of A

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Answer

Rearranging the equation from the previous step to find PQ (x) in terms of A:

$A = 10x + 30$

Subtract 30 from both sides:

$A - 30 = 10x$

Now divide both sides by 10:

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

Thus, the length of PQ in terms of A is:

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

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