Using three straight lines which intersect at three different points, we can create the figure called ‘Triangle,’ which represents the three angles. Among all the different types of triangles the most symmetrical is the equilateral triangle, and thanks to its symmetry, measurement of it is easy to calculate using the area of equilateral triangle formula.

There are now many educational platforms like Cuemath, which provide a very good understanding of Maths in general and geometry in specific wherein one can learn about all different types of triangles. In this article, we will focus on the equilateral triangle and how to calculate its area.

The different kinds of possible triangles are equilateral, right isosceles, obtuse isosceles, acute isosceles, right scalene, obtuse scalene, and acute scalene. All these triangles are different from each other depending upon whether all the three angles are the same or two angles are the same, any one angle is 90 degrees, or if any one of the angles is more than 90 degrees. It is noteworthy to remember that the sum of all the three interior angles of a triangle is always 180 degrees. It is also important to consider that the angles of a triangle and the sides of a triangle are proportional to each other such that the side in front of the smallest angle is the smallest and the side opposite the largest angle is the largest side in the triangle. Thus if we have a triangle that has got two equal angles, then it also has got two equal sides such a triangle is called Isosceles triangle.

In an equilateral triangle, all the three angles are equal, and since the sum of the three angles in the triangle is equal to 180 degrees, we can calculate that all the three angles of an equilateral triangle are always 60 degrees. Since all three angles of the triangle are equal thus all the three sides of the triangle also should be equal.

The equilateral triangle, thanks to its symmetry, is often used in many day-to-day applications, and in most of these cases, it is important to know the measure of the triangle that is how big it is. The area of the triangle is often considered the metric, which tells about how large the triangle is. The area of an equilateral triangle is

s^{2}/4 where ‘s’ is the length of the side.

So, using the formula, the length of the side of an equilateral triangle is 1 unit, then the area of such an equilateral triangle would be/4 square units. Do note that the area of the triangle is always expressed in square units. If we have an equilateral triangle with a length of the side as 2 units, then the area of such an equilateral triangle would be / 4 square units which is equal to square units. Let us dig deeper into the presence of irrational numbers like root 3 in the area of an equilateral triangle. Let us imagine a triangle drawn with its vertices having co-ordinates like (a,0), (-a,0), and (0,x). If we try to find the value of X in terms of a. If O is the origin, then as per Pythagoras theorem

OA^{2} + OC^{2} = AC^{2}

a^{2} + x^{2} = 4a^{2}

x^{2} = 3a^{2}

x = a so if a is a rational number then x is an irrational number.

The area of an equilateral triangle is easy to calculate as the triangle is symmetrical, and each side of the triangle is equal. If we draw a line from one vertex to the middle point of the opposite line, then we will have two right-angled triangles which would be equal in size. The area of a right-angled triangle is 1/2 * base * perpendicular.