Area of a triangle (conventional method)

Area of a triangle

The number of square units it takes to exactly fill the interior of a triangle.

Try this Drag the orange dots on each vertex to reshape the triangle. The formula shown will recalculate the area using this method.

(If there is no image below, see support page.)

Most common method

Usually called "half of base times height", the area of a triangle is given by the formula below.

where
b is the length of the base
a is the length of the corresponding altitude
See Triangle definition for a definition of base and altitude.

You can choose any side to be the base. The altitude must be the one corresponding to the base you choose. The altitude is the line perpendicular to the selected base from the opposite vertex.

In the figure above, one side has been chosen as the base and its corresponding altitude is shown.

Methods for finding triangle area

If you know:	Use this
Base and altitude	"Half base times height" method
All 3 sides	Heron's Formula
Two sides and included angle	Side-angle-side method
x,y coordinates of the vertices	Area of a triangle- by formula (Coordinate Geometry) Area of a triangle - box method (Coordinate Geometry)
The triangle is equilateral	Area of an equilateral triangle

Try this

In the figure above, drag the top of triangle carefully from left to right, but without moving it up or down. It's a little tricky, but as you drag the vertex, notice that the area does not change. The area is dependent on the base and height, and neither of them changes as you move the top vertex side-to-side.

Most common method

Methods for finding triangle area

Related triangle topics

General

Perimeter / Area

Triangle types

Triangle centers

Congruence and Similarity

Solving triangles

Triangle quizzes and exercises