Perimeter is the total distance around the outside of a polygon. It matters because it tells you how much border, fencing, trim, or edging is needed to go around a shape. Every side length contributes to the perimeter, so the main skill is identifying all outside edges and adding them accurately.
For middle-school geometry, perimeter connects measurement, addition, multiplication, and units in one useful idea.
For an irregular polygon, add each side length one by one because the sides may not match. For a regular polygon, all sides are equal, so you can multiply the side length by the number of sides. Composite figures require extra care because only the outer boundary counts, not lines inside the shape.
Perimeter is always measured in linear units such as cm, m, in, or ft, not square units.
Key Facts
- Perimeter means the total distance around the outside of a shape.
- Irregular polygon: P = side 1 + side 2 + side 3 + ...
- Regular polygon: P = n × s, where n is the number of sides and s is the side length.
- Rectangle: P = 2l + 2w, where l is length and w is width.
- Square: P = 4s, where s is the side length.
- Perimeter uses linear units such as cm, m, in, or ft, not square units.
Vocabulary
- Perimeter
- The total distance around the outside boundary of a two-dimensional shape.
- Polygon
- A closed two-dimensional shape made from straight line segments.
- Regular polygon
- A polygon with all sides equal in length and all angles equal in measure.
- Irregular polygon
- A polygon whose sides or angles are not all the same.
- Composite figure
- A shape made by combining two or more simpler shapes.
Common Mistakes to Avoid
- Using area units for perimeter is wrong because perimeter measures length around a boundary, so the units should be cm, m, in, or ft, not cm² or m².
- Adding only some of the sides is wrong because perimeter requires every outside side length to be included exactly once.
- Counting inside lines of a composite figure is wrong because perimeter only follows the outer edge of the entire figure.
- Assuming every polygon is regular is wrong because irregular polygons can have different side lengths that must be added separately.
Practice Questions
- 1 An irregular pentagon has side lengths 4 cm, 7 cm, 5 cm, 6 cm, and 8 cm. What is its perimeter?
- 2 A regular hexagon has side length 9 in. What is its perimeter?
- 3 A composite figure is made from two rectangles that touch along one full side. Explain why the shared side should not be counted in the perimeter.