Perimeter of an Equilateral Triangle

Have you ever wanted to put a boundary around something? Think about these real situations:

• Your school wants to put a fence around a triangular garden

• You need to buy a decorative border for a triangular picture frame

• A runner needs to know how far around a triangular running track

In each of these situations, we need the perimeter — the total length around the shape.

An equilateral triangle is a triangle in which:

• All three sides are equal in length.

• All three angles are equal (each is 60°).

For an equilateral triangle with side length = s

P = s + s + s

   = 3 × s

Perimeter = 3 × Length of one side

Problem: An equilateral triangular frame has a perimeter of 27 cm. What is the length of each side?

Solution:

• Perimeter = 27 cm

• We know: P = 3s

• So: 27 = 3s

• Divide both sides by 3: s = 27 ÷ 3

• s = 9 cm

Answer: Each side is 9 cm long.

Problem: A school wants to build a fence around a triangular garden. The triangular garden is equilateral with each side measuring 4 meters. How much fencing material is needed?

Solution:

• Each side of triangle = 4 meters

• It's an equilateral triangle, so all sides are equal 

• Perimeter = 3 × 4 = 12 meters

Answer: The school needs 12 meters of fencing material.

• An equilateral triangle has 3 equal sides

• For equilateral triangles: Perimeter = 3 × side length

• Use the formula: P = 3s (where s = length of one side)

• Always include the unit of measurement (cm, m, mm, etc.)

• If the perimeter P is known, the side length s = P ÷ 3.