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+---- Thread: Geometry & Area Cheat-Sheet — All the Key Formulas (/showthread.php?tid=64)
Geometry & Area Cheat-Sheet — All the Key Formulas - Leejohnston - 11-13-2025
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.