Boundary Math Example 2

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Example 2

medium
What is the boundary of a square with vertices (0,0)(0,0), (4,0)(4,0), (4,4)(4,4), (0,4)(0,4)? Find the perimeter of the boundary and determine whether the point (4,2)(4, 2) is on the boundary, interior, or exterior.

Solution

  1. 1
    Step 1: The boundary of the square consists of its four sides: the segments connecting the vertices in order.
  2. 2
    Step 2: Perimeter (boundary length) =4×4=16= 4 \times 4 = 16 units.
  3. 3
    Step 3: Point (4,2)(4, 2): it lies on the segment from (4,0)(4,0) to (4,4)(4,4) (the right side), which is part of the boundary. So (4,2)(4, 2) is on the boundary.

Answer

Boundary == four sides of the square; perimeter =16= 16 units; (4,2)(4,2) is on the boundary.
The boundary of a polygon is its perimeter — the set of all edge points. A point is on the boundary if it lies exactly on an edge or vertex. Interior points are strictly inside; exterior points are outside. Boundaries separate regions.

About Boundary

The edge or outline that separates the interior of a region from its exterior; the set of points on the dividing border.

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