What Is A Pentagon And The Real Life Examples of Real Pentagon?
The Pentagon can be defined as a polygon having five distinctive sides. It is also known as 5-gon. A Pentagon or a 5-gon can be made by connecting up straight lines on a flat surface that are of different angles. The word Pentagon has come out from a Greek word which means a shape having 5 distinctive sides. The size of the Pentagon and joined in such a way that gives self-intersect itself and the internal angles of a pentagon sum up to be 540 degrees. However, a pentagon that is self-intersecting is regularly known as Pentagram. For a regular pentagon, each of its interior angles is 180 degrees. A regular Pentagon also has two kinds of symmetry of each 5 lines they are reflection symmetry and rotational symmetry. The reflection and rotational symmetry have degrees of the order of 72 degrees, 44 degrees, 216 degrees, and 288 degrees. Again, for a regular pentagon, the diagonals of the Pentagon are convex and therefore have a golden ratio of its sides. For understanding golden ratios, one must at first understand what is a convex and concave Pentagon, a convex Pentagon is nothing but a pentagon whose vertices point outwards whereas for a concave Pentagon the vertices of the Pentagon points inwards. There are different forms of a polygon such as squares, rectangles, triangles, hexagons, etc. It is very important to understand shapes in geometry to properly understand their real-life applications for real-life situations. people who fail in understanding the actual essence of different kinds of shapes and how they are used for bringing in changes in real-life situations face problems regarding solving different types of practical challenges.
Finding area, height, and width of a regular pentagon
The height and the width of a pentagon are defined in a way that the height can be saved as the distance of an opposite vertex to one side of the Pentagon whereas the width of the Pentagon can be defined as measuring the distance between any two points which equals to the total length of the diagonal of the Pentagon. It is very crucial to understand the usefulness of Pentagons in real life as there come numerous situations and opportunities in which pentagons can be used for solving critical cases related to constructions or any other real-life jobs. There exist certain equations which tell how the height with and the diagonals of a pentagon can be measured which is shown below:
For finding out the area of a regular pentagon one must have the lengths of the sides as well as the apothem of the Pentagon. Is described as a line that is joint from the midpoint of a pentagon to one of the sides of the Pentagon, and for calculating the area of the total Pentagon one must know the length of the apothem. For a pentagon or any other shape, the sites of the shape are generally considered as s, and similarly, that distance of the apothegm is signified as a. For calculating the area a pentagon is first divided into five distinctive triangles by connecting the radius from each vertex to the center. This way 5 lines of the radius can be drawn in a regular pentagon. After dividing the Pentagon into five distinctive triangles the height of those distinct triangles is calculated and determined. And therefore the area of the triangles is calculated which is done by using the formula A=½*b*h, here 'a' is defined as the area of the triangle, 'b' is defined as the base of the triangle and 'he is the height of the triangle. In this case, the base of the triangle is equivalent to the Pentagon's length of its side and the height of a triangle is the apothem's length.
“ Area of the Pentagon = perimeter × apothem / 2”
The above-stated situation was of one kind but there can be a situation in which the length of the epithelium is not known but the length of the sides are known in such cases what one should do is described here. Firstly as in the above case, the Pentagon is to be divided into distinctive triangles and then each of the triangles and further divided into two right-angled triangles. The central angle of the Pentagon is 360 degrees, the base will be calculated as half of the total length of each side of the Pentagon and the length of the apothegm will be calculated by dividing the base length by tan 36. But if in case the perimeter of the Pentagon is known then the area of the Pentagon can be calculated by multiplying half with the perimeter and the apothem (½*p*a).
Real-life examples of Pentagon
Understanding the use of shapes and the use of the Pentagon is very crucial for people to solve real-life problems. There are various examples of pentagons in real life. One of the most prominent examples of pentagons in real life is the man-made Pentagon structure in the United States. People have taken the Pentagon for creating attractive models such as infrastructural models for years. Also, so the shape of a pentagon is widely used for creating a home plate in baseball which depicts the shape of an irregular pentagon. The most important factor is that nature has also depicted the Pentagon in one of its most beautiful creations the morning glories. Another example can be ladyfingers which fall in vegetables is when chopped off gives out the shape of a regular pentagon. From the segment of fruits, star fruit is a very prominent example of the Pentagon in real life. Other than that, a sea star is also a real-life example of the Pentagon. Lastly, there are minerals that also can be provided as a strong example of the Pentagon; they are Ho- Mg- Zn icosahedral quasicrystal. All the above mentioned are strong real-life examples of the Pentagon, therefore it is very important to understand the intricacies of the Pentagon and how it can be depicted in real-life scenarios.