Geometry: calculating areas and solids

In short: With a few formulas, perimeter, area and volume of the most important figures and solids can be calculated. This is needed in everyday life, for example when painting, tiling or packing.

In more detail: Areas are given in square metres, volumes in cubic metres or litres.

In detail

• Rectangle: Area A = a · b; perimeter P = 2(a + b).
• Triangle: A = (b · h) / 2.
• Circle: A = π · r²; C = 2 · π · r (π ≈ 3.14159).
• Trapezoid: A = (a + c) / 2 · h.
• Cuboid: Volume V = a · b · c; surface area S = 2(ab + ac + bc).
• Cylinder: V = π · r² · h.
• Sphere: V = 4/3 · π · r³; S = 4 · π · r².
• Units: 1 m³ = 1000 litres; 1 m² = 10,000 cm² (satz-des-pythagoras-anwenden).