Area is a measure of a flat surface. The measurement of the surface of three-dimensional objects is generally called surface area. The concept of "plane figure" in the definition is limited by "plane", which makes it less extensive and less inclusive.

For example, for a country, its area is a figure with a certain size surrounded by the boundary line on the surface of the spherical object of the earth, but it is not a plane; A cylinder's side is "flat" only when it is unfolded, and its own state is curved. It can be seen that the area is a measure of the area on a plane or surface, and it is not limited to "plane graphics".

Heron (or hero) of Alexandria found the so-called Heron formula in the triangle, and a proof in Metrica's book written about 60 years ago can be found in his book. Some people think that Archimedes knew this formula two centuries ago. Because Metrica is a collection of mathematical knowledge available in the ancient world, it is possible that this formula is earlier than the references in this book.

In 499, aryabhata, a great mathematician and astronomer in the classical times of Indian mathematics and Indian astronomy, expressed the area of a triangle as half the height of Aryabhatiya.

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In the 7th century AD, Brahmagupta developed a formula, which is now called Brahmagupta formula, to calculate the area of a circular quadrilateral on its side (the quadrilateral is engraved on a circle). 1842, German mathematicians Karandon Bretschneider and Karl Georg Christian von Staudt independently discovered a formula called Bretschneider formula, which can be applied to any quadrilateral area.