GCSE Edexcel Maths Coordinate Geometry: The diagram shows rectangle STUV

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

Question 8

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 8 - 2022 - Paper 3

Step 1

Find the area of trapezium QUVR

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Answer

To find the area of trapezium QUVR, we first identify the lengths of the parallel sides. The top base QU measures 5 cm and the bottom base SR measures 3 + 2x = (2x + 3) cm. The height of the trapezium, which is the distance between the two parallel bases, is defined by length of SV (4 cm).

The formula for the area A of a trapezium is given by:
$A = \frac{1}{2} (b_1 + b_2) \cdot h$
where $b_1$ and $b_2$ are the lengths of the parallel sides and $h$ is the height. Thus, we have:

$A = \frac{1}{2} (5 + (2x + 3)) \cdot 4$
Substituting this into the formula yields:
$A = \frac{1}{2} (2x + 8) \cdot 4 = (x + 4) \cdot 4 = 4x + 16$ .

Step 2

Simplify the equation

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Answer

Next, we substitute the trapezium area calculated into the equation and we could add the areas of the triangles that make up QUVR:

$A = \text{Area of triangles} + A_{rectangle}$
Adding the additional areas:

Area of triangle QTU
where height is 2x and base is the difference in lengths of SV and QU, yielding:
$Area_{QTU} = \frac{1}{2} (b \cdot h) = \frac{1}{2} ((4 - 2x) \cdot (2x)) = 4x - 2x^2$

Now adding the area of the rectangle STUV which is 12 cm² (width of 3 cm and length of 4 cm). Thus via summation, we establish:

$A = (4x + 16) + (4x - 2x^2) + 12 = 2x^2 + 20x$ .

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

Worked Solution & Example Answer:The diagram shows rectangle STUV - Edexcel - GCSE Maths - Question 8 - 2022 - Paper 3

Find the area of trapezium QUVR

Simplify the equation

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