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Here is a shape with all its measurements in centimetres - Edexcel - GCSE Maths - Question 17 - 2021 - Paper 1

Question 17

Here is a shape with all its measurements in centimetres. The area of the shape is A cm² Show that A = 2x² + 24x + 46.

Worked Solution & Example Answer:Here is a shape with all its measurements in centimetres - Edexcel - GCSE Maths - Question 17 - 2021 - Paper 1

Step 1

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Answer

To find the area of the shape, we first need to identify its dimensions:

The width of the entire shape is given by the expression: 2x + 6.
The height can be determined by summing the vertical parts: (x + 11) + 4 + (x + 1).

Thus, the complete height expression is:

$Height = (x + 11) + 4 + (x + 1) = 2x + 16$

Now, the area A can be calculated as follows:

$A = Width \times Height$

Substituting the values we found: $A = (2x + 6)(2x + 16)$

Step 2

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Answer

Now we will expand the expression for the area:

Distributing each term in the first expression across the second: $A = 2x(2x) + 2x(16) + 6(2x) + 6(16)$ $A = 4x^2 + 32x + 12x + 96$
Combining like terms: $A = 4x^2 + 44x + 96$

Step 3

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Answer

To rewrite the area in the form specified in the question:

Thus we have shown that: $A = 2x^2 + 24x + 46$

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