Geometry
Calculators, worked examples and guides — from area and perimeter through to Pythagoras' theorem, volume and circle geometry.
Learning about Geometry
The key idea: geometry is the maths of shape, space and measurement. Most geometry comes down to knowing a handful of rules (formulae) and applying them systematically. Label everything, write the formula first, then substitute.
Type 1 — Area of a triangle
"Find the area of a triangle with base 8cm and height 5cm"
Formula: Area = ½ × base × height
Step 1: ½ × 8 × 5 = 20cm²
Shortcut: Half of base × height — or think of it as half of the surrounding rectangle
Type 2 — Pythagoras theorem
"A right triangle has legs 3cm and 4cm. Find the hypotenuse."
Formula: a² + b² = c²
Step 1: 3² + 4² = 9 + 16 = 25
Step 2: c = √25 = 5cm
Shortcut: Remember the 3-4-5 and 5-12-13 Pythagorean triples — they come up repeatedly
Type 3 — Volume of a cylinder
"Radius 3cm, height 10cm. Find the volume."
Formula: V = πr²h
Step 1: r² = 9
Step 2: π × 9 × 10 = 90π ≈ 282.7cm³
Shortcut: Always square the radius BEFORE multiplying by π and h
Geometry Formula Sheet & Rules
Need a printable revision sheet? Access 2D area and perimeter formulas, 3D volume and surface area equations, circle theorems, and Pythagoras theorem with step-by-step worked examples and custom print export.
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Geometry Questions Answered
What is geometry?
Geometry is the branch of mathematics concerned with shapes, sizes, angles and the properties of space. It ranges from basic area and perimeter through to vectors and circle theorems.
What is Pythagoras theorem?
In any right-angled triangle, the square of the hypotenuse (longest side) equals the sum of squares of the other two sides: a² + b² = c².
How do I find the area of a circle?
Use the formula A = πr², where r is the radius (half the diameter). If given the diameter, divide by 2 first.
What is the difference between perimeter and area?
Perimeter is the total distance around the outside of a shape, measured in cm or m. Area is the amount of surface inside, measured in cm² or m².
What is a vector in geometry?
A vector describes movement — it has both magnitude (size) and direction. In secondary school geometry, vectors describe translations and are used to prove geometric relationships.