Practice Boundary in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The edge or outline that separates the interior of a region from its exterior; the set of points on the dividing border.
A fence around a yard—it marks exactly where 'inside the yard' ends and 'outside' begins.
Example 1
easyDraw a circle. What is the boundary of the circle (the disk region)? What is the interior? Use everyday language.
Example 2
mediumWhat is the boundary of a square with vertices (0,0), (4,0), (4,4), (0,4)? Find the perimeter of the boundary and determine whether the point (4, 2) is on the boundary, interior, or exterior.
Example 3
easyA country is enclosed by a border. Name what the border represents geometrically (boundary, interior, or exterior) for each region: (a) inside the country, (b) the border itself, (c) the neighbouring country.
Example 4
mediumThe region R is defined by the inequalities x \geq 0, y \geq 0, and x + y \leq 6. Describe the boundary of R and find its perimeter.