Geometry

Angles

An angle is formed where two lines meet at a point (called the vertex). Angles are measured in degrees (°).

Angle type	Size
Acute	Less than 90°
Right	Exactly 90°
Obtuse	Between 90° and 180°
Straight	Exactly 180°
Reflex	Greater than 180°

Angles on a straight line add up to 180°. Angles in a full turn add up to 360°. Angles in a triangle always add up to 180°.

Types of Triangles

By sides:

• Equilateral — all 3 sides equal, all angles = 60°
• Isosceles — 2 sides equal, 2 angles equal
• Scalene — no sides equal, no angles equal

By angles:

• Right-angled — one angle is exactly 90°
• Acute — all angles less than 90°
• Obtuse — one angle greater than 90°

Quadrilaterals

Shape	Properties
Square	4 equal sides, 4 right angles
Rectangle	Opposite sides equal, 4 right angles
Rhombus	4 equal sides, opposite angles equal
Parallelogram	Opposite sides parallel and equal
Trapezium	One pair of parallel sides

Perimeter

Perimeter is the total distance around the outside of a shape.

Rectangle: P = 2 × (length + width) = 2(l + w) Square: P = 4 × side Triangle: P = side₁ + side₂ + side₃

Example: Rectangle, l = 8, w = 3 P = 2(8 + 3) = 2 × 11 = 22

Area

Area is the amount of space inside a 2D shape.

Shape	Formula
Rectangle	A = length × width
Square	A = side²
Triangle	A = ½ × base × height
Circle	A = π × r²

Example: Rectangle, l = 9, w = 4 A = 9 × 4 = 36

Circles

• Radius (r) — distance from centre to edge
• Diameter (d) — distance across the circle = 2r
• Circumference — perimeter of a circle = 2πr ≈ 2 × 3.14 × r
• Area = πr² ≈ 3.14 × r²