Forming Equations from Shapes (Edexcel IGCSE Maths)

Spec point — 4.2E

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

Exam Hint 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 $3x+1$ cm and a width of $2x-5$ cm.

Its perimeter is equal to 22 cm.

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

Answer:

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

$2(3x+1)+2(2x--5)$

Expand the brackets

$6x+2+4x-10$

Simplify by collecting like terms

$10x-8$

This perimeter is 22, so set this expression equal to 22

$10x--8=22$

Solve this equation by adding 8 then dividing by 10

$\begin{gathered} 10 x & = 22 + 8 \\ 10 x & = 30 \\ x = \frac{30}{10} \\ x = 3 \end{gathered}$

$x=3$

(b) Find the area of the rectangle.

Answer:

The area of a rectangle is its length multiplied by is width Substitute the value of x from part (a) into the length and width given in the question

length is 3 × 3 + 1 = 10

width is 2 × 3 - 5 = 1

Find the area (multiply length by width)

10 × 1

Include the correct units for area

Final answer: Area = 10 cm²