Isosceles triangleVEXQOMIRA / GEOMETRY 05
Isosceles triangle Vexqomira

Formulas, without the guesswork.

Choose a relationship from the measurements you know. The variable names below belong to each calculator; a letter can have a different role in another method. π is evaluated using the browser’s full numerical constant, rather than replacing it with 3.14.

Equal side and base

h = √(a²−b²/4); A = bh/2

Inputs: Equal side a (length units); Base b (length units).

Apply this formula ↗

Base and height

a = √(h²+b²/4)

Inputs: Base b (length units); Height h (length units).

Apply this formula ↗

Equal side and vertex angle

b = 2a sin(θ/2)

Inputs: Equal side a (length units); Vertex angle θ (degrees).

Apply this formula ↗

Perimeter and base

a = (P−b)/2; P > 2b

Inputs: Perimeter P (length units); Base b (length units).

Apply this formula ↗

Reading the notation

√ means a square root, ∛ means a cube root, and a superscript ² or ³ means a square or cube. Sine, cosine and tangent use angles converted from entered degrees. Where an inverse trigonometric function is used, its displayed angle is converted back to degrees. The ellipse perimeter is approximate; other formula labels describe the ideal mathematical model.

Vertex angle means the angle between the equal sides. The base is not necessarily the longest side.

Reference reading: Isosceles triangle at Wolfram MathWorld.