Equilateral Triangle Calculator
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Equilateral Triangle
About Equilateral Triangles
An equilateral triangle is a triangle where all three sides are equal in length and all three angles are equal to 60 degrees. It's a special case of an isosceles triangle and is the most symmetrical triangle.
Key Properties
- All three sides are equal (s = s = s)
- All three angles are 60°
- Has three lines of symmetry
- Has rotational symmetry of order 3
- The height, median, angle bisector, and perpendicular bisector are all the same line
Formulas
- Height: h = (s√3) / 2
- Area: A = (s²√3) / 4
- Perimeter: P = 3s
- Inradius: r = (s√3) / 6 = h / 3
- Circumradius: R = (s√3) / 3 = 2h / 3
Frequently Asked Questions
What makes an equilateral triangle special?
All sides are equal length and all angles are 60°. It has the highest symmetry of any triangle with three lines of symmetry and 120° rotational symmetry.
How do you find the height of an equilateral triangle?
The height is h = (s√3)/2, where s is the side length. This comes from creating a 30-60-90 right triangle when you draw the height.
What is the area formula for an equilateral triangle?
Area = (s²√3)/4, where s is the side length. This simplifies the general triangle area formula for the equilateral case.
How many lines of symmetry does it have?
An equilateral triangle has exactly 3 lines of symmetry, each running from a vertex to the midpoint of the opposite side.
What is the relationship between inradius and circumradius?
The circumradius is exactly twice the inradius. If r is the inradius, then R = 2r. Also, R = 2h/3 and r = h/3.
Can I calculate everything from just the side length?
Yes, if you know the side length, you can calculate every other property of the equilateral triangle using the standard formulas.
Is an equilateral triangle also isosceles?
Yes, an equilateral triangle is a special case of an isosceles triangle where all three sides are equal, not just two.
Why are all angles exactly 60 degrees?
Since all angles in a triangle sum to 180° and all three angles are equal in an equilateral triangle, each angle must be 180° ÷ 3 = 60°.