Equilateral Triangles
Equilateral triangles have all three sides exactly the same length. Because their sides are the same length, the three angles of an equilateral triangle are also all the same size, so they're each one third of 360 degrees, or 60 degrees. All three angles of any equilateral triangle are 60 degrees, no matter how big or small the triangle is. It works the other way around, too - if all the angles are 60 degrees, then the triangle has to be equilateral, and all three sides will be the same length. Even if you only know that two of the angles are each 60 degrees, then the third angle also has to be 60 degrees, and the triangle has to be equilateral.
To figure out the perimeter of an equilateral triangle, you just add together the lengths of the three sides - or, because all three sides are the same, just measure one side and multiply by three.
Equilateral triangles also have some other interesting features. They're all bilaterally symmetrical - you can draw a line down the middle and they'll be the same on both sides. In fact, they're bilaterally symmetrical three different ways.
To figure out the area of an equilateral triangle when you know how long one side is, you need the Pythagorean Theorem. Draw a line from one corner to the middle of the opposite side, so that it makes a right angle (the two lines are perpendicular to each other). Now you have split your equilateral triangle into two right triangles. Use the Pythagorean Theorem to figure out how long the new line is. That is the height of your triangle. Multiply that by the length of the side, and then divide by two to get the area of your equilateral triangle.
If you stack six equilateral triangles together, you can make a hexagon. Do you see how the inside angles of the triangles add up to 360?
All equilateral triangles are also isoceles triangles, which have other interesting features.
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