Perimeter and Area of Plane Figures
79. The Area Concept · boundary plus interior
The rectangle's area is defined by its boundary and interior.
The area of a closed 2D figure is the amount of surface it covers. It is measured in square units (cm², m², …). Area is the size of the interior region bounded by the figure's sides.
What this lesson covers
Try to break it
Try moving P and Q. Notice how P stays on the boundary while Q explores the interior. The area combines both!
How you build it
Construct a rectangle with interior and boundary points.
- Draw a rectangle using the rectangle tool.
- Place a point on the boundary of your rectangle.
- Place a point inside the rectangle.
The proof, step by step
Prove that the area is the region enclosed by the boundary of the figure.
- The boundary is the length of the perimeter enclosing the shape.
- The interior is the region enclosed by the boundary.
- Area is the combination of the boundary and the interior.
Worked example
According to the definition, the area of any plane surface is the length of its boundary plus its ______.
Area is defined as the length of the boundary plus the interior of the plane surface.
- Perimeter
- Interior — correct
- Diagonal
- Vertex