Area of Triangle Formula

This figure illustrates the area of a triangle formula.

Formula

Summary

The area of a triangle is given by one-half multiplied by the base and height.

Expression Description
The area of the triangle.
The base length of the triangle.
The height length of the triangle.

Usage

The area of a triangle is calculated using the length of its base and the lenght of its height. For example, the area of a triangle with a base of and a height of is equal to to units squared as shown in the expressions below:

The formula can be derived using geometry and the area of a rectangle formula[1].

Examples

Example 1

area of triangle base 4 height 3

This example demonstrates how to calculate the area of a of triangle with a base of 4 and a height of 3.

Steps

  1. Start by setting up the formula.

  2. Substitute the base and height into the formula.

  3. Evaluate the multiplication.

  4. Evaluate the multiplication.

    THe area of the triangle is equal to units squared.

Example 2

area of triangle base 4 height 2

This example demonstrates how to calculate the area of a of triangle with a base of 4 and a height of 2.

Steps

  1. Start by setting up the formula.

  2. Substitute the base and height into the formula.

  3. Evaluate the multiplication.

  4. Evaluate the multiplication.

    THe area of the triangle is equal to units squared.

Example 3

area of triangle base 5 height 4

This example demonstrates how to calculate the area of a of triangle with a base of 5 and a height of 4.

Steps

  1. Start by setting up the formula.

  2. Substitute the base and height into the formula.

  3. Evaluate the multiplication.

  4. Evaluate the multiplication.

    THe area of the triangle is equal to units squared.

Explanation

The area of a triangle formula can be derived using a combination of geometry and the area of a rectangle formula [1]. The three cases of the derivation are correspond to three triangle types: right triangle, acute triangle and obtuse triangle.

References

  1. Derive Area of Triangle Formula
    Wumbo (internal)