All the core geometry formulas on one page. Keep it next to your homework.
Triangles
- Area: A = ½ × base × height
- Perimeter: P = a + b + c
- Pythagorean theorem (right triangle): a² + b² = c²
- Angles: the three angles add up to 180°
Quadrilaterals
- Square: A = s², P = 4s
- Rectangle: A = l × w, P = 2(l + w)
- Parallelogram: A = base × height
- Trapezoid: A = ½ × (a + b) × height
- Angles: the four angles add up to 360°
Circles
- Circumference: C = 2πr = πd
- Area: A = πr²
- Arc length: (θ / 360) × 2πr
- Sector area: (θ / 360) × πr²
3D shapes
- Cube: V = s³, surface area = 6s²
- Rectangular prism: V = l × w × h, surface area = 2(lw + lh + wh)
- Cylinder: V = πr²h, surface area = 2πr² + 2πrh
- Cone: V = ⅓πr²h
- Sphere: V = ⁴⁄₃πr³, surface area = 4πr²
- Pyramid: V = ⅓ × base area × height
Coordinate geometry
- Distance: d = √((x₂ − x₁)² + (y₂ − y₁)²)
- Midpoint: ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
- Slope: m = (y₂ − y₁) / (x₂ − x₁)
Polygons
- Sum of interior angles: (n − 2) × 180°
- Each angle of a regular polygon: (n − 2) × 180° / n
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