Free · Mathematical relationships

Isosceles Triangle Base from Equal Leg and Height

The altitude to the base bisects an isosceles triangle into two congruent right triangles. The equal leg must exceed the perpendicular height for a positive base.

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Formula and method

With known = 3, a = 5, h = 4, base = 6, area = 12.

b = 2√(a²−h²); A = bh/2

Worked example

Enter these known values and leave the other values blank.

I know...: 3
Leg (B): 5 cm
Height: 4 cm

Semiperimeter: 8 cm
Circumradius: 3.125 cm
Inradius: 1.5 cm
Base (A): 6 cm

Assumptions and limitations

The altitude to the base bisects an isosceles triangle into two congruent right triangles. The equal leg must exceed the perpendicular height for a positive base.
Enter enough independent values and clear the quantity being solved. Locks preserve known values; contradictory inputs can make the system inconsistent. Unit controls convert physical quantities rather than merely changing their labels.
Displayed precision is numerical rounding, not an estimate of measurement uncertainty.

Common questions

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Clear the missing value, enter the independent known values and retain compatible units. A nonunique inverse may require another known value.

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