What geometry calculates
Geometry measures the space taken up by shapes. For plane shapes, the area is the surface inside and the perimeter is the outline. For solids, the volume is the space occupied and the surface area is the total of all outer faces.
Formulas used
Rectangle: A = width × height. Circle: A = π × r² and C = 2 × π × r. Triangle from three sides: Heron's formula, A = √(s(s−a)(s−b)(s−c)), where s is half the perimeter. Cylinder: V = π × r² × h. Cone: V = π × r² × h / 3. Sphere: V = 4/3 × π × r³.
Units of measurement
Area multiplies two length measurements, so it comes out in square units, while volume multiplies three, coming out in cubic units. Use the same unit in every field: if the sides are in meters, the area comes in m² and the volume in m³.
Practical example
A cylindrical water tank with a 0.5 m radius and 1.2 m height holds about 0.9425 m³, or roughly 942 liters. A rectangular pool 8 m by 4 m and 1.5 m deep holds 48 m³, or 48,000 liters.