Equilateral triangle area
Equilateral triangle area A = √3/4·a²: enter the side length to get the area plus height, perimeter, inradius and circumradius; values are rounded to 6 decimals and a non-positive side is rejected.
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Result
One quantity per line, ready to copy.
Enter a side length to calculate
What this tool does
- Check the area and height of an equilateral part for sheet material or cutting.
- Compare how the area grows with the side length — it scales with the square, so doubling the side multiplies the area by four.
- Verify the formulas: area √3/4·a², height √3/2·a, circumradius √3/3·a.
Example
Input
3
Output
边长 3 的等边三角形面积：3.897114 高 √3/2·a：2.598076 周长 3a：9 内切圆半径 √3/6·a：0.866025 外接圆半径 √3/3·a：1.732051 长度单位 u，面积 u²，体积 u³
For side 2 the area is √3 ≈ 1.732051, the height √3 ≈ 1.732051, the perimeter 6, the inradius √3/3 ≈ 0.577350 and the circumradius 2√3/3 ≈ 1.154701 — all canonical.
Frequently asked questions
Why does the area formula contain √3?
Splitting the triangle along its height gives two 30-60-90 right triangles, so the height is √3/2·a and base × height / 2 yields √3/4·a².
How do the two radii relate?
In an equilateral triangle the circumradius is exactly twice the inradius (√3/3·a versus √3/6·a), a property unique to this shape.
What if the side is 0?
It reports an error. A zero side collapses the triangle into a point — the formula still evaluates but the answer is meaningless, so non-positive input is rejected.
Keywords：等边三角形正三角形面积equilateral triangle三角形面积几何计算边长