Perimeter of triangle

A triangle has three sides. Its perimeter is simply the sum of the lengths of all three sides. The formula is the same for every triangle – no matter how wide, tall, or slanted.

The formula

We call the sides side a, side b, and side c.

P = a + b + c

You add three numbers – done.

Three types of triangles

In the practice you will meet three types of triangles. The formula is the same; the side lengths behave differently.

Equilateral triangle

All three sides are equal. Knowing one side means you know all three.

If the side is 7 cm, the perimeter is:

P = 7 + 7 + 7 = 21 cm

Or as a shortcut: P = 3 · 7 = 21 cm.

Isosceles triangle

Two sides are equal (the legs), and one is different (the base). The legs may be longer or shorter than the base.

If the legs are 8 cm and the base is 6 cm, the perimeter is:

P = 8 + 8 + 6 = 22 cm

Scalene triangle

All three sides are different. There is no shortcut – you just add.

If a triangle has sides 5 cm, 7 cm, and 9 cm, the perimeter is:

P = 5 + 7 + 9 = 21 cm

A rule every triangle must satisfy

For three lengths to form a real triangle, the sum of any two sides must be greater than the third side. You cannot make a triangle with sides 2 cm, 3 cm, and 10 cm – the two shorter sides together don't reach across the longest one. The practice generator always respects this rule, so every triangle it produces can really be drawn.

Worked example

A gardener has a triangular flower bed. Its sides are 4 m, 6 m, and 7 m. How many meters of fence does she need to surround it?

The fence runs along the perimeter:

P = 4 + 6 + 7 = 17 m

She needs 17 meters of fence.

Common mistakes

For an equilateral triangle the problem only states one number. Some students forget to add three equal sides. Always remember: multiply by three, don't take the value just once.
For an isosceles triangle, students sometimes count the base twice instead of the legs. Look carefully at which two sides are equal.

Practice

The generator picks one of the three triangle types at random. It always builds a triangle that can really be drawn.

Generator: Perimeter of triangle