Perimeter , the boundary

If an ant walks around the edge of a chapati and returns to where it started, the distance it covered is the perimeter of the chapati. Perimeter is simply the total length of the boundary of a shape.

What is this?

To find the perimeter of any shape with straight sides, add up the lengths of all the sides.

For a rectangle with length 5 m and breadth 3 m, the four sides are 5, 3, 5, 3. Perimeter = 5 + 3 + 5 + 3 = 16 m.

We can shortcut this. A rectangle has 2 lengths and 2 breadths. So:

$\text{Perimeter of rectangle} = 2 \times (\text{length} + \text{breadth})$

For a square, all 4 sides are equal. So:

$\text{Perimeter of square} = 4 \times \text{side}$

For any other shape , pentagon, triangle, irregular , just add up all sides.

Perimeter is always measured in length units: cm, m, km. It has nothing to do with what is "inside" the shape, only the boundary.

We use perimeter when we want to put a fence around a field, a frame around a photograph, lace around a tablecloth, string around a kite. Anything along the edge.

Worked examples

Example 1. A rectangular farm is 80 m long and 60 m wide. Perimeter?

• 2 × (80 + 60) = 2 × 140 = 280 m.

Example 2. A square room has each side 4 m. Perimeter?

• 4 × 4 = 16 m.

Example 3. A triangular garden has sides 6 m, 8 m, 10 m. Perimeter?

• 6 + 8 + 10 = 24 m.

Try it

1. Rectangle: length 12 cm, breadth 7 cm. Perimeter?
2. Square: side 9 m. Perimeter?
3. Triangle: 5 cm, 6 cm, 7 cm. Perimeter?
4. A garden 25 m × 15 m needs a fence. How much fencing is needed?
5. The perimeter of a square is 36 m. Find one side.

Hands-on

Room boundary. Measure the four sides of your room with a tape measure. Add them up. This is the perimeter , the length of border tile or curtain rod you'd need.

Photo frame. Measure the four sides of a photo frame at home. Add them , that is the length of moulding used to make the frame.