grunnflate

Grunnflate is a term used in geometry and architecture to describe the base surface of a three‑dimensional object. It refers to the plane figure on which the solid rests and from which its height is measured, effectively the footprint of the shape. The grunnflate is the base against which other dimensions are defined and often the starting point for calculating volume and area.

In geometry, the grunnflate determines key properties of solids. For prisms and pyramids (and cones in the sense of base shapes), the grunnflate is the polygon or circle that serves as the base. The volume is calculated from the grunnflate area A_g and the height h: for a prism, V = A_g × h; for a pyramid or cone, V = (1/3) × A_g × h. The shape of the grunnflate (square, rectangle, triangle, circle) influences the remaining dimensions and the computation of A_g.

In architecture and construction, grunnflate is often used synonymously with the building footprint or base area—the ground area occupied by a structure. It is important for land use planning, foundation design, and zoning considerations.

Examples: a rectangular prism with base 4 by 3 units has grunnflate area 12 square units; a cone with base radius r has grunnflate area πr^2; a cylinder’s grunnflate is a circle with area πr^2.

Note: Some Norwegian texts use grunnflate interchangeably with bunnflate, though contexts may distinguish between the bottom surface and the base used for volume calculations.