Equilateral Triangle Formulas
As we know that equilateral triangle has all three angles equal in measure and all three sides equal in length. Based on these properties equilateral triangle formulas are defined. An equilateral triangle has a regular shape. The word 'Equilateral' is made up of two words: "Equi" which means equal and "Lateral" which means sides. Because all of its sides are equal, an equilateral triangle is also known as a geometric figure or regular triangle. We consider a most common formula of a triangle as:
An equilateral triangle’s perimeter.
An equilateral triangle's area.
An equilateral triangle's height.
Height of Equilateral Triangle
By using the Pythagoras theorem we can determine the height of an equilateral triangle. It is also known as the altitude of an equilateral triangle. We all know that all the sides are equal to an equilateral triangle. If we divide the triangle into two equal parts it forms two equal right triangles and it drops an altitude from the apex of the triangle to the base. Hence, from the above description, we can know the height of the triangle which is an equilateral triangle, as h =√3a/2
The Centroid of the Equilateral Triangle
At the centre of the triangle lies the centroid of the equilateral triangle. As we know all angles and sides are equal in length, so it is easy to find the centroid of it.
We need to draw from the opposite sides perpendiculars to each vertex of the triangle. These need to intersect each other at a common point and perpendicular should be all equal which is termed centroid.
The Circumcenter of a Triangle
The point of intersection of perpendicular bisectors of the side is the circumcenter of an equilateral triangle. Through all the three vertices of the triangle here the circumcircle passes.
When the circumcenter of a triangle coincides with any of the orthocenter, incenter or centroid, then it is called an equilateral triangle.
Geometry in Real Life – Triangle
For both architects and curious students, triangles possess several key advantages that make them ideal such as these shapes are structurally sound, easy to apply, incredibly common and used in everyday life.
Its shape, which spreads forces equally between its three sides, derives the strength of a triangle. Triangles are stable, as they are rigid inherently, the three sides reinforcing each other no matter what type of triangle is used in a structure (equilateral, isosceles, or scalene). The angles of a triangle will deform and buckle before the sides give away, discovered and explained by one thoughtful person. To deform a triangle without destroying it in the process simply put there's no way. They must also budget enough imaginary funds to buy sufficient gumdrops and toothpicks to span a river, not only do students sketch out the design.
FAQs on Maths Equilateral Triangle
1. What is the radius of the circumscribed circle of the equilateral triangle?
R= a/√3, where ‘a’ denotes the length of the side of vertices of a given equilateral triangle. The center of the circle is called the circumcenter and the radius of the circumcircle is termed the circumradius. The circumscribed circle or circumcircle of a triangle is a circle that passes through all the vertices and sides of the triangle. The backbone of all construction circles. We all know that a triangle is a geometric construction of straight three lines and three angles may be equal or may not be equal in measures.
2. What is the altitude from any side of the triangle?
h= √3/2×a, H is the height of the triangle here and the other portion is base by (2* A or Area). AD, CF, and BE with sides AB, CA, and BC are the altitude or height of the triangle. Hence the segment from the vertex of the triangle of any kind, if the sum of all sides is more than the sum of all the three given altitudes AB + BC + AC > AD + BE + CF, defines altitude. For example, the area is 49 sq. units and the length of the base is 7 units then the altitude is h= 2 * 49 / 7 = 14 units.
3. How to construct an equilateral triangle?
First of all, pull out a straight line segment and put the tip of the compass in any of the ends. Now let your compass draw an arc from that point to another. Redo the same technique to the other side of the line segment. At the end join the point of intersection of the two arcs. You will be ready with an equilateral triangle. The equilateral triangle is the triangle in which all sides have equal length; it is also equiangular i.e. angles are also equal.
4. If you are given all the angles equal. Will it be an equilateral triangle?
Let ∆ABC be an equilateral triangle whose all the angles are equal i.e. <A=<B=<C that makes 180°.You are given to prove that it is an equilateral triangle.
Let, you are not given <A. You just have <B and <C. We know that if the angles of a triangle are equal then their opposite sides will also be similar. Therefore, AB=AC.
Now in the next case, let's suppose you are not familiar with <C. As you did above the same method that will be applied here is BC=AC. Therefore, AB=BC=AC. Hence, all the sides are equal and as a result, given ∆ABC is an equilateral triangle.
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