Geometry is kind of like the foundation for everything else you learn in math classes. In other words, it’s like if you were learning how to build a house without using math, you wouldn’t end up with anything at all. In this article, let us study the area of the scalene triangle. This article will primarily focus on Euclidean geometry because that is what most people are familiar with.

How to Find the Area of a Scalene Triangle?
Michael Dziedzic

A triangle is a polygon with three straight lines called “sides.” Triangle can be called the first of the closed shapes that the lines form when connected to one another. In the Euclidean space, the sum of the internal angles of a triangle is always 180 degrees. This enables the measurement of any triangle’s third angle to be determined from the measurements of the first two angles. An angle that is a linear pair (and hence supplementary) to an interior angle of a triangle is called an external angle.

Since the three lines of a triangle can be of the different or the same length, depending on their measurements and the symmetry, if any, that the triangle possesses, there are several different classifications of the triangles. Equilateral, isosceles, right-angled, scalene are some of the various names given to the triangles depending on their properties.

To summarize what these triangles mean, equilateral is the name given to a triangle that has all the sides as equal and has each internal angle also equal, measuring as sixty degrees. An isosceles triangle has two of its sides as equal. A right-angled triangle has its two sides aligned at right angles or perpendicular to one other, area of the right triangle formula hence becomes easy as the base and height of the triangle are easily measurable due to being a right angle triangle. A scalene triangle has all of its three sides unequal, or they all measure differently, and hence all the internal angles also measure differently.

One postulate in geometry about the triangles states that according to the triangle inequality, the lengths of any two triangle sides must be more than or equal to the length of the third side. Only a degenerate triangle with collinear vertices may have that total equal to the length of the third side. It’s impossible for the amount to be smaller than the third side’s length.

After the classification of these triangular figures, the mathematicians also thought of the measurable aspects of them, which would aid in problem-solving. The two major measurable aspects in geometry are usually the area and the perimeter of the figure. The area gives us the amount of space acquired by the shape in the two-dimensional space, while the perimeter gives the total periphery of the shape or given form.

Hence if we talk of the scalene triangle’s area, we can find it with the help of a formula called Heron’s formula. For that, first, we have to find the perimeter of the triangle, which will be the sum of three sides, now a term ‘s’ is used in the formula, which is called the semi perimeter of the triangle, so we divide the perimeter into half to get the value of ‘s’.

And then proceed towards the actual area formula, which is equal to the square root of [s(s-a)(s-b)(s-c)] where a, b, c are the three of the sides of the triangle.

The triangular structure is much easier to fit closer to each other than any other shape and hence requires less space. Due to its properties, it is also used immensely in engineering and architecture.

To explore more on area calculations of scalene triangles, the students can refer to math worksheets which will give them enough practice on geometry problems. These worksheets are free to download from the Cuemath website.