Area of square and parallelogram
Before proceeding to finding the area of square, one should endeavor to understand the basic concept behind the terminologies involved here – the Area, and a Square. Area is known as a simple measurement of the quantity of space contained in a two-dimensional object. Area can be calculated simply by the multiplication of two numbers, however, it sometimes requires more than just the multiplication of two numbers. This is when irregular shapes come in. But when we have a 2-dimensional object, then we make do with just the multiplication of the two regular sides – the length and the width
There are different methods for finding the area of different objects and shapes. and some of these different shapes include:
- Squares
- Rectangles
- Triangles
- Circles
- Cylinder
- Pyramids
- Parallelograms
- Trapezoid
- Regular polygons
But for the sake of this study, we will be laying more emphasis on the area of square.
Before we understand the formula for computing the area of square, we need to know what exactly a square is. Everyone has a sense of shapes, but once we go deeper into the shape in order to unravel the mystery behind the formula for every geometrical figure we will be able to imagine the broader picture. A square is known as a regular quadrilateral having all of its four angles and sides equal. Squares may differ in the length of their sides but you must know that all their four angles are right angles. So in other words, what we know is the a square has all sides equal and the angle between all sides is the same if seen from adjacent sides. Between two adjacent sides in a square, the angle is a perfect 90 degrees which is also known as a right angle. Hence, when you are calculating the area of square, you are basically computing how much space the geometrical figure occupies by considering the dimensions of the structure. In this case, the area of square is computed by calculating the product of two equal sides. Hence, if the side of a square is “a”, then the area of square would be a2. Hence, all you need to know is that all the sides of a square are equal otherwise it will not be called as a square.
A Square And Its Basic Properties
It is important to note that a square can exist as a rhombus, a parallelogram or as a rectangle if the length of its sides, right angles and diagonals are the same. Below are other facts to note:
- A square has all its four sides of the same length and they are equal to AB=BC=CD=AD : AB=BC=CD=AD
- A square has all its four angles as right angles: 90°=∠ABC=∠BCD=∠DAB=∠CDA
- A square has its opposite sides parallel: BC||AD, AB||CD
- A square has the sum of its angle equal to 360°: ∠ABC+∠BCD+∠DAB+∠CDA=360°
- A square must have diagonals of the same length: BD=AC
- A square is divided into two equal symmetrical area by each of its diagonal
- The right angles of a square is intersected by its diagonals and the other half is shared: BD┴AC BO=AO=DO=CO=d/2
- The angle of a square is divided into half by each of its diagonal, which denotes that they play the role of a bisector to the square’s angles: ΔABC=ΔBCD=ΔDAB=ΔCDA
∠ABC=∠BCD=∠ACD=∠BDA=∠CAB=∠DBC=∠DAB=∠CDA=45°
- The diagonals intersection point is called the square’s center and the inscribed circle’s circumcenter and circumscribed circle.
- The square is divided by both diagonals into four triangles that are equal and these triangles are both isosceles rectangular in shape: ΔBOC=ΔAOB=ΔDOA=ΔCOD
Before we head to calculating the area of square, one needs to understand what a diagonal is for the sake of squares that we know only their diagonals. The diagonal of a square is knows as any segment connecting a square’s two vertices opposite angles together. We should know that any square’s diagonal is √2 times greater than its sides.
There are various conditions for finding the diagonal of a square and they are:
- In terms of the side of the square, we can find its diagonal using: d=a*√2
- In terms of the area of square, we can find its diagonal using: d=√2A
- In terms of the perimeter of the square, we can find its diagonal using: d=P/(2√2)
- In terms of the circumradius of the square, we can find its diagonal using: d=2R
- In terms of the square’s circumcircle diameter, we can find its diagonal using: d=Dc
- In terms of the square’s radius, we can find its diagonal using: d=2r√2
- In terms of the square’s incircle diameter, we can find its diagonal using: d=Di√2
- In terms of the square’s segment length, we can find its diagonal using: d=l(2√10/5)
Below is a detailed illustration to emphasize on how to find the area of square :
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- If we know the length of a side, then the area of square will be equal to the square of the side: A=a2
- If we know the diagonal length, then the area of square will be equal to half of the squared diagonal: A=½d2
Where:
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- A is the area of square
- a is the length of a side
- and d is the diagonal length
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Many a times, you will be made to work on an analytical essay for college assignments and this would require you to do ample research before proceeding ahead with the topic.
Many people tend to get confused between squares and rectangles although the difference lies in their sizes only. The difference between a square and a rectangle is that a rectangle has a different length and breadth whereas a square has all sides equal. Thus, if the question comes to you that if a rectangle has a length equal to the breadth, then you should know that this shouldn’t be called a rectangle in the first place. But one thing that remains common between a rectangle and a square is the angle between two adjacent sides which remains at 90 degrees. Similarly, the area of a rectangle can be computed by calculating the product of length and breadth:
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- The result of the lengths of two sides (width and height) equals the area of the triangle: A=a*b
- Here A is the area of rectangle
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- a and b are the lengths of the sides (the triangle’s width and height).
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Area of Parallelogram and Rhombus
When it comes to coordinate geometry, you will come across plenty of thesis examples in books as well as web forums which will help you develop a better understanding of the topic. The courseworks for coordinate geometry are quite vast for college students since there are lots of topics that are interrelated and you will have to do a lot of research to understand the concepts.
So what exactly is the difference between a parallelogram and a rectangle? If you notice a parallelogram, you will see that opposite sides are parallel to each other, but the angle between two adjacent sides is neither 90 degrees nor zero. It can vary according to the shape of the parallelogram. Going by the definition, parallelogram happens to be a polygon which is four-sided and the opposites sides tend to be parallel to each other having same angles. Coming to the area of a parallelogram, you will have to perform a multiplication of the height with the base of the parallelogram.
Similar to the parallelogram, we have the trapezoid that has 5 sides. Now the catch over here is that only two sides are parallel to each other. The other two sides might or might not be parallel to each other. Now when it comes to calculating the area of a trapezoid, two of the parallel sides have to be added and then multiplied with the height of the trapezoid and finally, dividing the result by 2. Once the entire result has been devised, the value you get will be the area of the trapezoid.
Drafting an engineering paper on area of square
First of all, you need to know about an engineering paper which includes proper formatting, citations and the references used to draft the paper. There are lots of ways in which an engineering paper can be written and it totally depends on the individual understanding of the person. But usually, the beginners are recommended to go through a standard format and once they have gained enough experience with one standard, they will be able to develop a better understanding of the subject and according to that, they can make modifications to the format according to their convenience.
The first rule for writing a case study analysis is to ensure that the information you have applies to the topic and helps you in explaining the concept. An engineering paper needs to be composed in a proper format without which, it will lose its impact factor. While writing an engineering paper on the area of square, you will have to research how the formula came into being and what are the components of the formula. Once you have explained each of the elements properly, then you will have to explain to the reader how the elements are related to the square and justify how the formula accurately measures the total area of square.
Thus, this article has briefly described how the formula for calculating the area of square came into being and also discusses other polygons such as the trapezoid, the parallelogram and rectangle. But in order to write the best essay, you need to have the best references which will give you a better understanding of the whole topic and will help you in explaining to the readers how the elements justify the formula used to calculate the area of square.
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