Perimeter and Area of Plane Figures
78. The Triple Side · Perimeter of an equilateral triangle
The perimeter is always exactly three times the side length.
Perimeter of an equilateral triangle = 3 × side. Since all three sides are equal, just add them: P = a + a + a = 3a.
What this lesson covers
Try to break it
Try to break it: drag the slider to change the side length. The perimeter is always exactly 3 times the side. You can't break this relationship; it's true by definition of an equilateral triangle.
How you build it
Construct an equilateral triangle.
- Place point A, the first corner of the triangle.
- Place point B. The segment AB will be the base of the triangle.
- Draw the segment from A to B.
- Set the compass opening to AB — click A, then B. Draw an arc centred at A.
- With the compass still set to AB, draw an arc centred at B — it crosses the arc from A.
- Mark point C where the two arcs cross, above AB. Now CA = CB = AB.
- Draw the segment from A to C.
- Draw the segment from B to C. All three sides are equal — ABC is an equilateral triangle.
The proof, step by step
Prove that the perimeter of an equilateral triangle is 3 × side.
- In an equilateral triangle, all three sides are equal by definition.
- The perimeter is the total distance around the triangle, which is the sum of its three sides.
- Since all sides are equal, Perimeter = side + side + side = 3 × side.
Worked example
An equilateral triangle has a side length of 15 cm. Find its perimeter.
Perimeter = 3 × side = 3 × 15 cm = 45 cm.
- 30 cm
- 45 cm — correct
- 60 cm
- 22.5 cm