Equilateral Triangle Calculator

If you’re a math geek, then you probably enjoy doing calculations as much as possible. Unfortunately, most of us don’t have the time to sit down and do all the math we want: there’s just too many important things to do! That’s why we created this equilateral triangle calculator for you. It allows you to input any desired variable and get instant results—no more tedious number-crunching!

An equilateral triangle is a triangle that has three equal sides. In this post, we’ll talk about the properties of equilateral triangles, how to solve them, and how to use our free online calculator.

What is a triangle?

A triangle is a polygon with three sides and three vertices (corners). Triangles can be classified according to their sides, as acute (less than 90 degrees), right (90 degrees), obtuse (more than 90 degrees) or scalene triangles.

What is an equilateral triangle?

An equilateral triangle is a triangle with all sides of the same length. Equilateral triangles are also called isosceles triangles because the two sides of an isosceles triangle are equal in length, but they’re not always equiangular, or equal angles.

A right triangle is a type of right angle triangle. Right triangles have one 90° angle (the right angle), and two smaller angles that add up to 90° as well. The side opposite the right angle in a right triangle is called its hypotenuse. The other two sides are called legs or catheti.

Properties of equilateral triangles

The following properties apply to equilateral triangles:

• All three sides are the same length.
• All three angles are the same.
• All three sides are congruent (that is, they all have the same measure).
• The three pairs of opposite sides form two pairs of congruent triangles that determine each other’s altitude and base.

The height of an equilateral triangle

The height of an equilateral triangle is the distance from the midpoint of a side to the opposite vertex.

This means that if you take any side, divide it into two equal parts, and then extend both sections until they intersect at the opposite vertex, you’ll have found the height.

Since all sides are equal in length and all angles are 60 degrees, we can also say that one half of any given side will always be equal to its corresponding height.

Equilateral triangle surface area

To calculate the surface area of an equilateral triangle, we use the formula:

A = \frac {\sqrt {3} \times a^2} {4}

So, for an example, if you had an equilateral triangle, whose sides were equal to 10cm, its surface area would be equal to:

A = \frac {\sqrt {3} \times (10cm)^2}{4} \\ A = 43.301 cm^2

How to use the equilateral triangle calculator

We say this often, but the equilateral triangle really is simple to use because there is only one thing you need to enter in order to get your desired result. That one thing you need to enter is the side length (a).

Once you enter the side length, everything else is easily calculable, because the calculator can basically draw the triangle. So, it will calculate:

• The height
• The area
• The perimeter
• Semiperimeter
• The circumcircle radius (the circle that can be drawn outside of the triangle, that touches all the vertices of the triangle)
• The incircle radius (the circle that can be drawn inside the triangle, that touches all sides of the triangle)
• The angles (they will always be 60 degrees)

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