Definition
Boundary
A boundary is the edge that separates a shape or region from what lies outside it.
What it means
Imagine tracing around a shape without shading its inside. Your finger follows the boundary. It tells where the region stops; it does not tell how much space the region covers.
Remember it
Boundary is the edge; perimeter is how long the closed edge is.
Example
A rectangle is 6 cm long and 3 cm wide. Its boundary is the four sides around it. Measuring along that boundary gives a perimeter of 6 + 3 + 6 + 3 = 18 cm.
Watch for
The boundary itself is geometric; a number such as 18 cm is a measurement of its total length, not the boundary.
Common mix-up
Do not mix up boundary with area: boundary is around the region, while area measures the region inside.
Exact meaning
A boundary is the edge, or set of edge points, separating a region from its exterior. For a closed two-dimensional shape, the perimeter is the total length measured along that boundary.