[Maths Class Notes] on Maths Equilateral Triangle Pdf for Exam

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.