[Leejohnston]

Geometry & Area Cheat-Sheet — All the Key Formulas

This is a quick, simple reference sheet for the GCSE geometry topics most learners struggle with.

Keep this one bookmarked — you’ll use it a lot.

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1. Perimeter Formulas

Rectangle: 
P = 2(length + width)

Square: 
P = 4 × side

Triangle (general): 
P = a + b + c

Circle (Circumference): 
C = 2πr 
or 
C = πd

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2. Area Formulas

Rectangle: 
A = length × width

Square: 
A = side²

Triangle: 
A = 1/2 × base × height

Parallelogram: 
A = base × height

Trapezium: 
A = 1/2 × (a + b) × height 
(where a and b are the two parallel sides)

Circle: 
A = πr²

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3. Surface Area Basics

Cuboid: 
SA = 2(lw + lh + wh)

Cube: 
SA = 6 × side²

Cylinder: 
SA = 2πr² + 2πrh 
(top + bottom + curved surface)

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4. Volume Formulas

Cuboid: 
V = length × width × height

Cube: 
V = side³

Cylinder: 
V = πr²h

Prism (any shape): 
V = area of cross-section × length

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5. Pythagoras’ Theorem

For right-angled triangles:

a² + b² = c² 
(c is the hypotenuse)

Example: 
If a = 3 and b = 4, then: 
c = 5

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6. Trigonometry Basics

Right-angled triangles only:

SOH CAH TOA

• Sin = Opposite / Hypotenuse 
• Cos = Adjacent / Hypotenuse 
• Tan = Opposite / Adjacent 

Example: 
sin(θ) = 3/5 → θ = sin⁻¹(3/5)

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7. Angles Quick Rules

• Straight line = 180° 
• Full turn = 360° 
• Right angle = 90° 
• Angles in a triangle = 180° 
• Angles in a quadrilateral = 360° 
• Opposite angles in parallel lines are equal 
• Corresponding angles are equal 
• Alternate angles are equal 

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8. Common Mistakes

❌ Mixing up radius and diameter 
❌ Forgetting the height must be perpendicular 
❌ Using the wrong trigonometry ratio 
❌ Using area formulas for volume 
❌ Forgetting units (cm², cm³, etc.) 

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Summary

Geometry becomes easy when you memorise:
• Perimeter 
• Area 
• Surface area 
• Volume 
• Pythagoras 
• Trigonometry 

Keep this cheat-sheet handy — it will save you in exams.