Equilateral Triangle Calculator — From Side Length
Area
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Perimeter
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Height
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Inradius
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Circumradius
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How to Calculate Equilateral Triangle Properties
An equilateral triangle has all three sides equal and all three angles equal to 60 degrees. Given just the side length s, you can derive every property. The area is (sqrt(3)/4) times s squared, and the height (altitude) is (sqrt(3)/2) times s.
The inradius (radius of the inscribed circle) is s divided by (2 times sqrt(3)), while the circumradius (radius of the circumscribed circle) is s divided by sqrt(3). The circumradius is always exactly twice the inradius in an equilateral triangle.
Equilateral triangles appear in engineering (truss structures), architecture (geodesic domes), road signs, and tiling patterns. They offer maximum symmetry among triangles and are the strongest triangular shape for load distribution.
Frequently Asked Questions
What is the area formula for an equilateral triangle?
The area is (sqrt(3)/4) times the side length squared: A = (sqrt(3)/4)(s squared). For a side of 10, the area is approximately 43.30 square units.
What are the angles of an equilateral triangle?
All three angles are exactly 60 degrees, summing to 180 degrees. This is what makes it equilateral (equal sides) and equiangular (equal angles).
How is the height of an equilateral triangle derived?
Drop a perpendicular from one vertex to the opposite side. This creates two 30-60-90 right triangles. Using the Pythagorean theorem: h = sqrt(s squared - (s/2) squared) = (sqrt(3)/2)(s).