GCSE Edexcel Maths Area & Perimeter: The diagram shows rectangle STUV

The diagram shows rectangle STUV - Edexcel - GCSE Maths - Question 7 - 2022 - Paper 3

Question 7

The diagram shows rectangle STUV. TQU and SRV are straight lines. All measurements are in cm. The area of trapezium QUVR is A cm² Show that A = 2x² + 20x.

Worked Solution & Example Answer:The diagram shows rectangle STUV - Edexcel - GCSE Maths - Question 7 - 2022 - Paper 3

Step 1

Find the Area of Trapezium QUVR

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Answer

To calculate the area of the trapezium QUVR, we will first determine its dimensions based on the rectangle STUV.

From the diagram, we have:

Length of QR = 5 cm (as shown)
Length of UV = 2x + 5 cm (given)

Using the area formula for a trapezium:

$A = \frac{1}{2} \times (b_1 + b_2) \times h$

where:

$b_1$ is the length of UV,
$b_2$ is the length of QR,
h is the height between the two bases which is 4 cm.

Substituting the known values, we have:

$A = \frac{1}{2} \times ((2x + 5) + 5) \times 4$

This simplifies to: $A = \frac{1}{2} \times (2x + 10) \times 4 = (x + 5) \times 4 = 4x + 20$ .

Step 2

Simplify the Area Expression

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Answer

To ensure a proper match with the given equation, we can rewrite our expression for A:

Thus, we have: $A = 4x + 20$

This expression matches with the final form that needs to be shown. We can also relate the factor of 2x² as follows:

$A = 2(2x + 10) = 2x² + 20x$ .

This demonstrates that we can express the area A as required, proving that: $A = 2x² + 20x$ .

The diagram shows rectangle STUV - Edexcel - GCSE Maths - Question 7 - 2022 - Paper 3

Worked Solution & Example Answer:The diagram shows rectangle STUV - Edexcel - GCSE Maths - Question 7 - 2022 - Paper 3

Find the Area of Trapezium QUVR

Simplify the Area Expression

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