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🔺 Triangles
Angles, perimeter & triangle facts.
⬛ Quadrilaterals
Rectangle, square, parallelogram & trapezium basics.
⭕ Circles
Radius/diameter, circumference & area.
🔺 Triangles — Angles, Perimeter & Properties
⬛ Quadrilaterals — Angles, Perimeter & Area
⭕ Circles — Radius, Diameter, Circumference & Area
Geometry Formulae – Triangles, Quadrilaterals & Circles
These are the most important geometry formulae students need for Years 7–10. Each section includes practice links and trusted explanations for deeper understanding.
1) Triangle Formulae
Triangle Angle Rule: The sum of interior angles in any triangle is 180°.
Angle Sum
A + B + C = 180°
A, B, C are the three interior angles.
Area of a Triangle
Area = ½ × base × height
Triangle Inequality
a + b > c
a + c > b
b + c > a
Pythagoras’ Theorem
a² + b² = c²
c is the hypotenuse (opposite the 90° angle).
Isosceles Triangle Rule
Equal sides → equal opposite angles
Equilateral Triangle
Each angle = 60°
External:
MathsIsFun – Triangle Rules
2) Quadrilateral Formulae
Quadrilateral Angle Rule: Interior angles add up to 360°.
Angle Sum
A + B + C + D = 360°
Area of Rectangle
Area = length × width
Area of Square
Area = side²
Area of Parallelogram
Area = base × height
Area of Trapezium
Area = ½ × (a + b) × h
Perimeter (Any Quadrilateral)
P = a + b + c + d
External:
Khan Academy – Polygons
3) Circle Formulae
Diameter
d = 2r
Circumference
C = 2πr
C = πd
Area of Circle
Area = πr²
Arc Length
Arc = (θ / 360°) × 2πr
Sector Area
(θ / 360°) × πr²
Angle Rule
Angle at centre = 2 × angle at circumference
External:
MathsIsFun – Circle Formulae
📌 Tip for students: Memorise the rules, then practise applying them using topic-based practice tests .
