The area of a triangle can be demonstrated, for example by means of the congruence of triangles, as half of the area of a parallelogram that has the same base length and height.A graphic derivation of the formula that avoids the usual procedure of doubling the area of the triangle and then halving it.
In geometry, calculating the area of a triangle is an elementary problem encountered often in many different situations. The best known and simplest formula is where b is the length of the base of the triangle, and h is the height or altitude of the triangle. The term "base" denotes any side, and "height" denotes the length of a perpendicular from the vertex opposite the base onto the line containing the base. Euclid proved that the area of a triangle is half that of a parallelogram with the same base and height in his book Elements in 300 BCE.[1] In 499 CE Aryabhata, used this illustrated method in the Aryabhatiya (section 2.6).[2]
Although simple, this formula is only useful if the height can be readily found, which is not always the case. For example, the land surveyor of a triangular field might find it relatively easy to measure the length of each side, but relatively difficult to construct a 'height'. Various methods may be used in practice, depending on what is known about the triangle. Other frequently used formulas for the area of a triangle use trigonometry, side lengths (Heron's formula), vectors, coordinates, line integrals, Pick's theorem, or other properties.[3]
^"Euclid's Proof of the Pythagorean Theorem | Synaptic". Central College. Retrieved 2023-07-12.
^The Āryabhaṭīya by Āryabhaṭa (translated into English by Walter Eugene Clark, 1930) hosted online by the Internet Archive.
^Weisstein, Eric W. "Triangle area". MathWorld.
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