omtrek

Omtrek is a Dutch term that refers to the boundary length around a two-dimensional shape. In English, it is commonly translated as perimeter, and for circles the related term circumference is often used. The omtrek is a one-dimensional measure of extent around the boundary, in contrast to area, which measures the two-dimensional size of the shape.

For common shapes, the omtrek is calculated as follows:

- Circle: omtrek = 2πr = πd, where r is the radius and d is the diameter.

- Rectangle: omtrek = 2(l + w), where l is length and w is width.

- Square: omtrek = 4s, where s is the side length.

- Regular n-gon: omtrek = n·a, where a is the side length.

More generally, the omtrek is the sum of all boundary segments of the shape. Shapes with curved boundaries require summing or integrating along the boundary.

Calculation and use:

The omtrek can be found by measuring the boundary directly or by adding known edge lengths. It is widely used in design, construction, and land surveying. In educational settings, problems often ask for the omtrek from given dimensions, with emphasis that omtrek is not the same as the enclosed area. For shapes with curved boundaries, exact results may rely on appropriate formulas, such as the circle’s circumference, rather than polygonal approximations.

See also perimeter, circumference, and area for related measurements in geometry.