Area of an equilateral triangle Geometry is one of the most important sciences that exist because it is used to solve many problems. This science was discovered by engineers and there are many geometric shapes such as triangles of all kinds. We will learn about the area of an equilateral triangle, so follow the following lines via the EGYPress website .
Information about engineering
Engineering is classified as one of the most important and prominent sciences that exist today because it includes a lot of science, theories, applications, mathematics and rules that are used to solve all different problems.
All of these rules, theories, and more happened through engineers figuring out how things work.
Not only that, a group consisting of all scientific uses that help in the discovery and realization of all scientific discoveries was discovered.
Currently, engineers, scientists, and inventors are inventing a lot of innovations that help in the development of human conditions in general.
But all the credit for these inventions and innovations goes in the end to the engineers because they take a very active role in showing all these innovations to the outside world.
As for the history of engineering, it is considered an integral part of the history of the existence of human civilization, which includes all the engineering functions carried out by engineers in various fields such as development, design and modification.
And some other more important areas and systems such as evaluation, testing, inspection, installation and maintenance that are carried out on various and various systems.
In addition to all this, all processes and materials are also specified, construction supervision and control, manufacturing and consulting services are also provided.
Providing consultancy services is one of the most important functions, services and responsibilities provided in the fields of engineering.
triangles
Triangles are one of the most important geometric shapes in geometry and have many uses.
As for the triangle, it is a three-sided triangle and consists of three geometric vertices. As Euclidean geometry mentioned, the sum of the measures of the interior angles of a triangle in Euclidean space is always 180 degrees.
Through these measurements, the measure of the third angle of any triangle of any kind is determined by looking at the two apparent angles.
In any triangle, there is an angle called the exterior angle of the triangle, and it is defined as the angle that represents a linear pair that is complementary to the interior angle of the triangle.
In addition, the measure of the exterior angles of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.
This is considered the exterior angle theorem the sum of the measures of the exterior angles of any triangle of any kind equals 360 degrees.
Triangles are of many types, but they differ in terms of the properties and details that each triangle includes.
triangle formation
A triangle consists of three straight segments, and these segments are called sides.
At the end of these straight segments there is a point, which is the point where the sides meet each other. These points are called vertices or angles.
Thus, a triangle has three angular or three vertices, and the sum of the measures of these angles is 180 degrees.
The smallest side of a triangle always corresponds to the smallest interior angle of the triangle.
The vertex of the triangle can be defined as the angle of the triangle, and each triangle has three vertices.
The rule is the drawn side that is not equal to the rest of the sides of the triangle, and this rule is used to calculate the area of the triangle.
The median of the triangle, which is the line extending from the vertex of the triangle to the middle of the opposite side, and each triangle has three of them, and all these sides intersect at one point called the central point of the triangle.
The height is defined as the column that extends from the vertex of the triangle to the base opposite it. Since there is a triangle that has three angles, then it has three heights as well, which is the product of the intersections of the heights with each other.
Types of triangles according to side lengths
The first type is the equilateral triangle, which is a triangle with all three sides of equal length.
All of its angles are also equal, and each angle measures 60 degrees.
The second type is the isosceles triangle, which is a triangle that has two sides of equal length and two angles of equal measure, and these two angles are the base angles.
The third type is a scalene triangle, which is a triangle that has no sides of equal length and no angles of equal measure either.
Types of Triangles According to Angles
The first type is an acute triangle, defined as a triangle whose angles are all less than 90 degrees.
An obtuse triangle is defined as a triangle that has an angle of greater than 90 degrees and is called obtuse angles.
A right-angled triangle is defined as a triangle consisting of three right angles, each angle measuring 90 degrees, and this type of triangle has several different types.
Types of right-angled triangle
A right triangle is a triangle that has three right angles, each of which measures 90 degrees.
The first type is a 90-45-45 triangle, which is a right-angled triangle and each of its angles is 45 degrees.
In addition, it is an isosceles triangle and the sides of this triangle are always in proportion, and this proportion is in the ratio 1:3√:2 and this ratio is constant in all right triangles.
The second type is 90-45-45 is a right-angled triangle, and one of its angles has a measure of 60 degrees, and the other angle is 30 degrees, and the third angle is the product of their addition and subtraction of the result from 180 degrees.
In this triangle, the sides of this triangle are in equilibrium with each other and this proportion is in the ratio 1:3√:2 and this ratio is constant.
General properties of a triangle
The sum of the measures of the angles of a triangle is 180 degrees.
The sum of any two sides of a triangle is greater than the length of the third side.
The difference between the lengths of any two sides of a triangle is less than the length of the third side.
The exterior angle of any triangle is equal to the sum of the two remote interior angles. This property is very famous and it is called the exterior angle property and it is present in all types of triangles.
The side opposite the largest angle in a triangle is the largest side.
If the opposite angles are in two triangles, then the sides are equal, and this is true in all types of triangles.
The area of any triangle is 0.5 base length * height.
The perimeter of any triangle is equal to the sum of all three sides of the triangle.
A triangle that has one angle greater than 90 degrees is called an obtuse angle triangle.
A triangle whose sum of all angles is less than 90 degrees is an acute angle triangle.
Properties of the median of a triangle
It bisects the vertex angles that are present from two equal sides in isosceles triangles and also in equilateral triangles.
In any triangle, there are three median lines that intersect at one point called this central point, or as it is called in English Centroid.
Each of these lines is divided the ratio is always constant in all triangles 2:1.
Each median of the triangles can be categorized into two separate but one area triangles.
Using Apollonius’ theorem, the length of the mean of the triangle can be calculated as follows.
m a = ((2b²+ 2g²-a²) ÷4) √.
or m b = ((2a²+2g²-b²) ÷4) √.
or m g = ((2a²+2a²-g²) ÷4) √.
Each symbol of this law can be known by understanding and reading the following.
m c is the length of the mean line going down from vertex c, c: the length of the side opposite the vertex c.
m b is the length of the mean line coming down from vertex b, b: the length of the side opposite vertex b.
m a is the length of the mean line coming down from vertex A, a: the length of the side opposite vertex A.
Properties of the height of a triangle
The height of the triangle can be, lie outside the triangle, or lie inside the triangle.
Each triangle has three possible heights, and each one extends from one of the vertices of the triangle.
The height from the vertex to the opposite side of the triangle is considered the shortest height.
All three altitudes always meet at one point, apart from the shape and type of a triangle.
