Geometry is the study of shape, distance, angles, symmetry, and specifically their measurements, and it is useful in architecture as well as design to measure the angles on buildings for construction purposes. In this article, let us have a look at heron’s formula and how it is useful in geometry.
We know that shapes are categorized according to the dimensions that each occupies, like a point has zero dimension, a line has one dimension (length), a plane has two dimensions (length and width), 3D objects have 3 dimensions (length, width, and height).
And hence, shapes are classified as polygons. A polygon is any shape with straight sides that meet at a common point called an ‘edge’ or ‘vertex’. A triangle is one type of polygon as it has three sides or lines, whereas a square or rectangle has four sides and is hence referred to as quadrilateral.
The complex geometry of shapes is used to describe other common mathematical topics and is closely related to many other subjects which study the shape of objects, like topology, linear algebra, algebra, calculus, and so on. Besides this, it’s useful in various applications in engineering fields.
Hence, considering the measurement aspect, geometry has huge implications in real life too, mathematicians have always come up with innovative theorems and formulas to ease out this measurement calculation of shapes, be it the area or the perimeter. Speaking of Heron’s formula, this is one such formula that helps in the calculation of the area of triangles in an easy way.
Heron (or Hero) of Alexandria is credited with the formula, and a demonstration can be found in his work Metrica. It has been hypothesized that Archimedes knew the formula more than two centuries before, and since Metrica is a compendium of old-world mathematical knowledge, it is probable that the formula predates the reference supplied in that work.
It is also said that the ancient Indian mathematician and astronomer Brahmagupta had already mentioned it at least half a millennium before. It may well be that Archimedes knew about this formula from his extensive studies in India during his time as a young man.
This formula is clever and intriguing proof to find the area of a triangle. When the lengths of all three sides of a triangle are known, the area of the triangle can be calculated. Unlike previous triangle area formulas, no angles or other distances in the triangle must be calculated first.
A thing to note here is that the cyclic quadrilaterals were used in Heron’s original proof.
Proceeding towards the formula, it says to first calculate the semi-perimeter of the triangle, which is denoted by s = (a + b + c)/2. Then, calculate the area, which will be the square root of the value [s(s-a)(s-b)(s-c)], where a, b, c are the respective sides of the given triangle.
Triangles can be considered to be the most simple shapes. They are also one of the basic building blocks of mathematics, and they have a wide range of applications. As a result, students are encouraged to practice using triangle worksheets in order to better understand the notion of triangles. According to studies, the worksheets have a strong link to mathematical reasoning, which is crucial for students.
Students should make use of this instructional tool because it can assist with a variety of skills, including problem-solving and thinking. Cuemath is one such website that offers a selection of triangle worksheets for both teachers and students. These are both easy to download and print. If they get stuck, students can use the answer keys that come with these worksheets, which provide extensive explanations of the solutions offered by Cuemath’s expert staff.