Measurement: Perimeter, Area, Surface Area & Volume

perimeter

If you walked all the way around the edge of a garden and came back to where you started, the total distance you covered is the perimeter. It is simply the length of the boundary of a flat figure — how much fencing you would need to enclose it.

For any polygon the perimeter is just the sum of the side lengths: walk around once and add up every side. A rectangle 3 by 5 has perimeter 3 + 5 + 3 + 5 = 16, which we usually write as 2(3 + 5) = 16 because opposite sides are equal. For a regular polygon with n equal sides of length s the perimeter is simply n times s. The same idea works for any closed figure; for a circle the boundary length has its own name, circumference.

Perimeter is a length, so it is measured in length units (cm, m, km) and never in square units — that is the trap people fall into, confusing it with area. Two figures can have the same perimeter but wildly different areas: a long thin 1-by-7 rectangle and a 4-by-4 square both have perimeter 16, yet the square encloses 16 square units while the thin one encloses only 7.

A triangular plot has sides 6 m, 8 m, and 10 m. Its perimeter is 6 + 8 + 10 = 24 m, so 24 m of fence will enclose it.

Perimeter adds up the boundary; you cannot tell the area from it alone.

Perimeter and area answer different questions; a bigger perimeter does not mean a bigger area, and they carry different units (length versus length squared).

Also called
boundary length邊界長度