Free · Geometry and function relationships

Isosceles Triangle Heights, Radii and Area

An isosceles triangle has equal legs. Its altitude to the base splits the base in half and forms two right triangles; the two base angles are equal.

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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.

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Formula and method

For base_b = 10, height_from_base_to_vertex_hb = 12, leg_a = 13, area = 60, perimeter = 36.

leg²=(base/2)²+height²; A=base×height/2

Worked example

Enter these known values and leave the other values blank.

Base (b)
10 cm
Height from base to vertex (hb)
12 cm
Leg (a)
13 cm
Height from leg to base corner (ha)
9.23 cm
Vertex angle (β)
45.24 deg
Base angle (α)
67.38 deg
Area
60 cm²
Perimeter
36 cm
Semiperimeter
18 cm
Circumradius
7.042 cm
Inradius
3.333 cm

Assumptions and limitations

  • An isosceles triangle has equal legs. Its altitude to the base splits the base in half and forms two right triangles; the two base angles are equal.
  • Clear the unknown field before solving. Locks preserve known quantities; an inverse may have multiple solutions and this model selects its principal branch.
  • Numerical rounding does not describe measurement uncertainty. Extremely large arguments or near-singular inverses can exceed the available precision; use moderate values for interpretable finite results.

Common questions

How do I enter a consistent set of values?

An isosceles triangle has equal legs. Its altitude to the base splits the base in half and forms two right triangles; the two base angles are equal.

Can I calculate a missing input?

Clear that field and provide enough independent known quantities. Output-only fields and nonunique inverse branches may need a different mode.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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