Understand the equilateral triangle

An equilateral triangle has three equal sides. In Euclidean geometry this also makes all three interior angles equal to 60 degrees. Specifying one positive side length fixes its size.

Properties that make the calculations work

An altitude bisects the opposite side and creates two 30–60–90 right triangles. The centroid, circumcentre, incentre and orthocentre coincide. The height is √3/2 times the side.

Where the model is useful

Use the forward calculator for triangular tiles and the inverse tools when a design specifies area, total edge length or height. All four tools use the same exact relationships before rounding the results.

Measure the right thing

The altitude is shorter than the side. An arbitrary triangle cannot use these formulas merely because two sides look similar.

Sketch the figure and mark every known measurement before choosing a calculator. A length measured along an edge is not automatically a perpendicular height. If a formula needs a radius, check that the value has not been measured across a full diameter. Write the unit beside each known quantity before entering it.

Scale and units

Multiplying every length by k multiplies any area by k². This is a useful check: doubling all dimensions cannot merely double an area. Inputs expressed in centimetres produce cm² for area; the unit selector relabels rather than converts entered numbers.

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Wolfram MathWorld: Equilateral triangle provides reference reading. Our summaries and examples are written for this portal and are not a specialist-reviewed textbook. Try a worked example or suggest a correction.