Area and Perimeter of Plane Figures
262. Perimeter vs. Area · Boundary length vs. surface measure
Perimeter measures the boundary length; Area measures the enclosed surface.
Perimeter is the total length of the boundary of a figure, measured in units of length; area is the amount of surface enclosed, measured in square units. Two figures can share a perimeter yet enclose different areas.
What this lesson covers
Try to break it
Drag A, B, or C to reshape the triangle. The perimeter (sum of the three side lengths) and the area (the shaded interior) change independently. Push C inward toward AB and the area shrinks while the perimeter can stay similar — perimeter and area are two separate measurements, and pinning one doesn't pin the other.
How you build it
Mark three corners — A, B, C — and join them into a triangle.
- Point tool: drop the first corner A anywhere.
- Point tool: drop the second corner B.
- Point tool: drop the third corner C, off the line AB.
- Segment tool: join A to B — one side of the boundary.
- Segment tool: join B to C.
- Segment tool: join C to A. The perimeter is AB + BC + CA — the boundary length; the area is the surface enclosed inside.
The proof, step by step
Prove that perimeter measures the boundary while area measures the enclosed surface.
- Perimeter is defined as the total length of the boundary enclosing a plane figure.
- Area is defined as the measure of the surface enclosed within that boundary.
- Perimeter uses linear units (cm, m), while Area uses square units (cm², m²).
Worked example
A rectangular garden measures 10 m in length and 6 m in width. What is the perimeter of the garden?
Perimeter of a rectangle = 2 × (length + width) = 2 × (10 + 6) = 2 × 16 = 32 m.
- 16 m
- 32 m — correct
- 60 m
- 120 m