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kotreny
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Where is it proven that the unit of area in Euclidean geometry must be a square with side=1? Or is it an axiom? Why not triangles or circles to represent area?
The Euclidean area is the measure of the size of a flat surface in a two-dimensional space. It is commonly referred to as the "amount of space inside a shape" and is usually measured in square units.
To calculate the Euclidean area of a shape, you need to multiply the length of its base by its height. For example, the area of a rectangle is calculated by multiplying its length by its width, while the area of a triangle is calculated by multiplying its base by its height and then dividing the result by 2.
Euclidean area is measured in square units because it is a two-dimensional measurement. This means that the area is represented by two units of length multiplied together, resulting in a unit of area that is squared.
Euclidean area is a fundamental concept in geometry as it allows us to measure and compare the sizes of different shapes. It is also an important tool in solving problems and proving theorems in geometry.
No, Euclidean area can only be measured in square units. This is because the concept of area is defined as the amount of space inside a two-dimensional shape, and it cannot be measured in any other units besides those that involve multiplying two units of length together.