# Perimeter

## Perimeter

Length of the boundary of a closed plane geometric figure.

### Formulas

Exact formula :

• Perimeter of a square of side length sP = 4s
• Perimeter of a rectangle having a length of L and a width of l : P = 2 × (L + l)
• Perimeter of a rhombus of side length s : P = 4s
• Perimeter of a parallelogram with adjacent sides a and b : P = 2 × (a + b)
• Perimeter (circumference C) of a circle of radius r : C = 2πr

Estimates of the perimeter P of regular polygons inscribed in a circle of radius r :

• Perimeter of an equilateral triangle : P ≈ 1.732r × 3 ≈ 5.196r
• Perimeter of a square : P ≈ 1.414r × 4
• Perimeter of a regular pentagon : P ≈ 1.176r × 5
• Perimeter of a regular hexagon : P = r × 6
• Perimeter of a regular octagon : P ≈ 0.765r × 8
• Perimeter of a regular decagon : P ≈ 0.618r × 10
• Perimeter of a regular dodecagon : P ≈ 0.518r × 12

The exact formula for calculating such a perimeter as a function of the radius r of the circumscribed circle is : 2$$nr$$ × sin($$\frac{π}{n}$$) where $$n$$ is the number of sides and $$r$$ is the length of the radius of the circumscribed circle.

• For the triangle : sin($$\frac{180}{3}$$) = sin(60) and  P = 2 × 3 × r × sin(60) and P ≈ 6r × 0.866 ≈ 5.196r
• The perimeters above have all been calculated using this method.

When the length of one of the sides of the regular polygon is given, it can be multiplied by the number of sides of the polygon.

### Examples

• The perimeter P of a square with a side length c of 3 cm is 12 cm, or : P = 4c = 4 × 3 = 12.
• The perimeter P of a rectangle whose length L is 8 cm and whose width l is 6 cm, is 28 cm, or :
P = 2 × (L + l) = 2 × (8 + 6) = 2 × 14 = 28.