Forming-Equations-From-Shapes Aqa Foundation

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Exam code:8300

Forming equations from shapes

How do I form equations from shapes?

You need to use all the information given on the diagram and any specific properties of that shape
Common 2D shapes that you should know properties for are
- Triangles: equilateral, isosceles, scalene, right-angled
- Quadrilaterals: square, rectangle, kite, rhombus, parallelogram, trapezium
You may be asked about perimeter, area or angles
You may be asked about polygons
- Regular vs irregular polygons
- Interior vs exterior angles
  - The sum of interior angles is 180(n-2) for an n-sided polygon
You may be asked about angles in parallel lines
- Alternative, corresponding and co-interior
You may be asked about 3D shapes involving surface area and volume
- Prisms have constant cross sections
  - Volume is cross-section area multiplied by length

Is there anything else that can help?

Sketch a diagram if none is given
Split up uncommon shapes into the sum or difference of common shapes
Look out for important extra information
- For example, a trapezium “with a line of symmetry”
With irregular shapes, assume all angles and lengths are different (unless told otherwise)
Put brackets around algebraic expressions when substituting them into geometric properties

Forming and solving an equation from an irregular polygon

Examiner Tips and Tricks

Read the question carefully – does it want an angle? perimeter? total area? curved surface area? etc.
For surface area and volume questions, check the list of formulas given in the exam.

Worked Example

A rectangle has a length of $3 x plus 1$ cm and a width of $2 x minus 5$ cm.

Its perimeter is equal to 22 cm.

(a) Use the above information to find the value of x.

The perimeter of a rectangle is 2 × length + 2 × width

$2 left parenthesis 3 x plus 1 right parenthesis plus 2 left parenthesis 2 x – 5 right parenthesis$

Expand the brackets

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Maths Gcse Aqa Foundation

Forming-Equations-From-Shapes Aqa Foundation