## Subjects

# The perimeter of a triangle

What is true for all triangles?

## The perimeter of a triangle

Triangle. Tri.. angle. A triangle is geometric shape with three straight sides, and three corners. Triangles can be very different, but all triangles have a few things in common: You calculate their perimeter in the same way.

You calculate their surface area in the same way. And the sum of their angles is always the same. We're only going to look at the perimeter now. You'll learn about area and angles another time. The perimeter is the distance all the way around the edge.

To keep this goat from escaping, you have to put up a fence. How much fencing material do you need to buy? Well, this fence has to follow the perimeter of this triangle-shaped pasture. And to get the perimeter of a triangle, you add the lengths of the three sides. 3 plus 4 plus 5 equals 12 meters of fence.

The perimeter is 12 meters. This applies to all triangles. If you call the sides a, b, and c, then the triangle's perimeter is a plus b plus c. This always works, for all triangles. And there are some triangles where it’s even easier.

Look at this triangle on the right. All three sides are exactly the same length. A triangle with three sides the same length is called an… … equilateral triangle. We show this by marking a short line through all the sides that are equal in length. With three equal sides, we can use multiplication instead of addition, if we want to.

If the sides are each 4 meters, then the perimeter equals three times 4 meters. Or more generally, if an equilateral triangle has sides of the length a, the perimeter equals three a. (Remember, you can miss out the multiplication sign, and just write 3 a) Look at the triangle on the left. This has two sides that are equal, and a third side of different length. Let’s mark the two sides that are equal with short lines. A triangle with two equal sides is called an… ...isosceles triangle.

And with two sides of 5 meters each, and a base of 3 meters, the perimeter is two times five plus 3, equals 13 meters. So if the equal sides are of length A, and the third side is of length B, the perimeter equals: two A plus B. Perimeter is the distance along a shape's outer edge. To calculate the perimeter of a triangle, add the lengths of the three sides. An isosceles triangle has two equal sides.

In an equilateral triangle all three sides are equal.