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Heron's formula

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Heron's formula

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formula for calculating the area of a triangle

AI overview

Heron's formula is a mathematical method for calculating the area of a triangle using only the lengths of its three sides, without needing to know the height. This formula is useful because it allows you to find a triangle's area whenever you know all three side lengths, which is often simpler than measuring the height directly.

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Described at

Heron's Formula for Triangular Area

personal.math.ubc.ca

Because the proof of Heron's Formula is "circuitous" and long, we'll divide the proof into three main parts. These congruences follow by AAS. Since corresponding parts of congruent triangles are congruent, we have Please don't be discouraged with the following algebra. These can be visualized using Figure 10.

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Encyclopedic overview

A triangle with sides a, b, and c In geometry, Heron's formula (or Hero's formula) gives the area of a triangle in terms of the three side lengths ⁠

a ,

Excerpted from Wikipedia’s “Heron's formula” article, available under the CC BY-SA 4.0 licence.

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