The triangle is considered the simplest polygon in plane geometry and the most important, taking into account the characteristics of its shape. Support structures are built in a triangular shape, due to the safety obtained.
Note the use of triangles
in the support of roofs.
As a polygon, the triangle has a perimeter (sum of the measurements of the sides) and an area. In the case of triangles, the area is measured through half the product of the base and the height, according to the formula: 
, with b base measurement and h height measurement. There are three models of triangles as to the measurement of their sides:
Scalene: The sides have different measurements.
Isosceles: It has two sides with equal measures.
Equilateral: has all sides with the same measure.
Our work will emphasize the area of an equilateral triangle. Note the triangle of vertices A, B and C with sides measuring The and height H.
In this case we do not know the height measurement, which should be calculated using the Pythagorean Theorem. Look:
According to the calculated height measurement h, we will determine the area of the equilateral triangle based on the following formula:
Note that the given expression calculates the area of any equilateral triangle based on the measurement of its side.
Example 1
Determine the area measurement of an equilateral triangular region, with sides measuring 12 meters in length.
The triangular region has an area measuring 36√3 meters.
Example 2
What is the lateral measurement of an equilateral triangle that has a total area measuring 100√3 cm²?
by Mark Noah
Graduated in Mathematics
Brazil School Team
See more!
Area of any triangle
Calculating the area of triangular regions.
plane geometry - Math - Brazil School
Source: Brazil School - https://brasilescola.uol.com.br/matematica/area-um-triangulo-equilatero.htm