Free · Triangle calculators 🔺

Equilateral Triangle Area and Perpendicular Height

Calculate equilateral triangle area and perpendicular height with retained unit controls, positive geometric roots and explicit inverse-branch assumptions.

  • Formula & worked example
  • Private in your browser
  • No signup
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

Worked inputs Side (a) = 4 give Height (h) = 3.4641016, Area (A) = 6.9282032. Values use the initial displayed units.

h = a√3/2; A = a²√3/4

Worked example

Enter these known values and leave the other values blank.

Side (a)
4 cm
Height (h)
3.464 cm
Area (A)
6.93 cm²

Assumptions and limitations

  • All three sides are equal. This workflow retains the side, altitude and enclosed-area controls; the positive geometric root recovers a side from area.
  • Lengths and areas are converted before calculation. Clear an unknown measurement instead of supplying conflicting dimensions.
  • Arithmetic uses 64 significant digits and full-precision π. Display rounding and measurement uncertainty are separate from the underlying arithmetic.

Common questions

Which measurements and inverse branch does this model use?

All three sides are equal. This workflow retains the side, altitude and enclosed-area controls; the positive geometric root recovers a side from area.

Is the height the same as a side length?

No. The perpendicular height is √3/2 times the side. Area is half the product of the side and that height.

References

The international acre is exactly 43560 square international feet; Bookify replaces the rounded captured area factor.

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