Perimeter and Area of Plane Figures
74. What is a Region? · Interior + Boundary = Region
The region is always the combination of the boundary and the interior.
The region enclosed by a closed figure is the set of all points inside it (the interior) plus the boundary itself. Both together form the region.
What this lesson covers
Try to break it
Try to separate the interior from the boundary! Drag the triangle's vertices — no matter the shape, the region is always interior plus boundary. It never breaks!
How you build it
Make a triangle to mark its region.
- Place point A, the first vertex of the triangle.
- Place point B, the second vertex.
- Place point C, the third vertex.
- Draw the side from A to B.
- Draw the side from B to C.
- Draw the side from C to A to complete the triangle.
The proof, step by step
Prove that a region is the interior together with its boundary.
- The boundary consists of the lines that enclose the figure.
- The interior is the part of the plane enclosed by the boundary.
- Region = Interior + Boundary.
Worked example
The interior of a figure along with its boundary is called its:
By definition, the interior of a figure along with its boundary is called the region of the figure.
- Perimeter
- Region — correct
- Area
- Symmetry