Geometry Intermediate

Triangle Area — Multiple Methods

Choose your method: base & height, Heron's formula, two sides and an angle, or three coordinate vertices (shoelace formula). Full step-by-step shown.

4 area methods

Step-by-step work

Live triangle graph

Input

Method

Base b

Height h

Try:

Side a

Side b

Side c

Try:

Side a

Side b

Included angle C (degrees)

Try:

Vertex A

x₁

y₁

Vertex B

x₂

y₂

Vertex C

x₃

y₃

Try:

Result

Select a method and enter values.

Step-by-Step Solution

Triangle Diagram

Four Area Formulas

A = ½ · b · h A = √(s(s-a)(s-b)(s-c)) [s=(a+b+c)/2] A = ½ · a · b · sin C A = ½|x₁(y₂-y₃)+x₂(y₃-y₁)+x₃(y₁-y₂)|

When to Use Each

Base & Height: You know perpendicular height.

Heron's: You know all three side lengths.

SAS: You know two sides and the angle between them.

Coordinate: Vertices are given as (x, y) points.

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