Introduction

A rectangle is a two-dimensional geometry figure which has four sides and four corners. The word rectangle comes from the Latin rectangulus, a combination of rectus (as an adjective, right, proper) and angulus (angle). It is one of the quadrilateral types in which opposite sides are parallel to each other, and each side meets another side at 90-degree angle. Some other types of quadrilateral are parallelograms, rhombus, square, etc. The line segments that join the opposite corners of a rectangle are called its diagonals. It’s a familiar two-dimensional figure that is commonly visible in day-to-day life. Some examples in real life that resemble a rectangle figure are Blackboard, Mobile Phones, TV, and Door.

Some elementary mathematical properties of a rectangle are as follows:

1. Each interior angle is equal to 90 degrees.
2. The diagonals of a rectangle bisect each other.
3. Opposite sides of a Rectangle are parallel to each other. 
4. The sum of all the interior angles is equal to 360 degrees.
5. The sum of the four exterior angles is equal to 360 degrees.
6. Both the diagonals are of the same length. 
7. If length is multiplied with the breadth of a rectangle or vice-versa, it gives the rectangle area. Area: a*b
8. The perimeter of a rectangle is: 2*(a+b)
9. The length of each diagonal of a Rectangle: (a2+b2)1/2
10. The diagonals of a rectangle bisect each other at different angles. One angle is acute, while another is obtuse. Note: If the two diagonals of a rectangle bisect each other at 90 degrees, then the rectangle is known as square 
11. It has two lines of reflectional symmetry and rotational symmetry of order 2 (through 180°).

Note: a and b are sides of a rectangle (for 7,8)

Some compelling facts about rectangle

• Every square is a rectangle, but every rectangle is not a square.
• All rectangles are parallelograms, but all parallelograms are not rectangles.
• The diagonals of a rectangle divide the rectangle into four triangles.

Applications of Rectangle

Everywhere around us, there are rectangular shapes more than any other shape in the world(~Catman). It took a significant amount of time for Ancient Greeks to figure out quadrilaterals and completely understand their properties. Pythagoras was the first person who drew the first-ever rectangle. It's easy to realize that the properties of a rectangle would just make life simpler.

Let's have a better grasp of the application aspect of a rectangle’s properties by making the life of Bob easier.

Consider Bob has just bought a new property and is very glad about the property’s design and finish. Though everything is looking beautiful and in-place, Bob caught sight of the back portion of the property and realized that the garden area is not up to the notch. He was never good at mathematics to his bad luck and could never think of applying mathematical properties in real-life. Now, we are familiar with the properties of a rectangle, so we decide to help bob by comprehending his requirements. 

Bob's Requirements

Bob loves his dog Bruno very much, at first, he wants to guard his garden by creating a fence around it so that his dog wouldn't be able to disturb him while he's working. Next thing, Bob wants to keep the English Ivy plant in his garden. He has already got three rectangular cases for growing plants. Last but not the least, Bob wants to have his inflatable swimming pool sits in the garden right beside his plants. Bob’s problem is that he is worried about how he should place his plants in the garden so that he can simply chill beside his plants right in the swimming pool on a summer day. Bob has managed to get dimensions of the following entities.

Garden: 10 X 8 metres

Plant growing case: 4 X 2 metres 

Inflatable swimming pool: 8 X 5 meters

Analysis

We understand Bob wants a fence around his garden area and since the layout of the garden is rectangular, so we figure out, we can easily use the rectangle's perimeter formula to calculate the amount of fence required to meet the purpose. Bingo, we are good with the first requirement of bob. The second requirement, Bob wants to grow English Ivy plants in the garden with enough space left so that he can easily place his favorite summer swimming pool in the garden as well. We are confident to calculate the area of any rectangular figure and can easily help Bob by letting him know whether he could chill on a summer day near his plant or not! We hope for the best and proceed to the calculations with dimensions as provided by Bob.

Fence Solution:

Perimeter of Garden = 2*(Length + Breadth)

= 2*(10 + 8)

= 36 metres

Hurray, We have actual measurements for the total fence needed so that Bob can work in his garden without being disturbed by his dog. 

Plant and Swimming Pool Solution:

Area of Garden = Length X Breadth 

= (10 X 8)

= 80 metres

We realize we have a total of 80 meters of area. 

Total area required for three plants = 3 X (Area required for one plant)

Area required for one plant = Length X Breadth 

= (4 X 2)

= 8 metres

Total area required for three plants = (3 X 8)

= 24 metres

Fingers Crossed,

Total area required for swimming pool = Length X Breadth 

= (8 X 6)

= 48 metres

Total area required for both plants and swimming pool = ( Total area required for three plants + Total area required for swimming pool )

= (24 + 48)

= 72 metres 

Total area left in the garden = (80 - 72)

= 8 metres 

Bingo, we have calculated the area required to serve both of the purposes, and the results are up to mark with Bob’s wish. Not just that, we have surprised him with an extra 8 meters of area left in the garden where maybe he can place his table and simply work with a nice and warm sunset view.

We have shared the results with Bob, and all of us are delighted to be good friends. And finally, all toast to "Friend in need is a friend indeed!".

Another good implication where properties of a rectangle can be used to help out our other friends. 

Suppose five best friends live in Goldfield's Regency. Since Goldfield Regency is a large residency and is quite famous in the town. There's is a delightful occasion as there's one guy's birthday out of five boys. Four boys except for the boy whose birthday is approaching, determine to plan for their best friend’s birthday bash. But, there's a problem, as it's summer, everyone is feeling lethargic and nobody out of all four boys wants to travel the extra distance to meet one another. So, their plan is getting deferred day by day. On one lucky day, one of them, preparing for his maths exam, unknowingly stumbled upon the solution to the problem they are facing. He realized, all four of them live at the corners of the Goldfield Regency, so the scenario comes to be a rectangular layout. Hence they can meet at the central confectionary because he just refreshed his knowledge that the diagonals of a rectangle are equal and bisect each other. In this way, all of them would need to cover equal distance and everyone would be glad to meet one another to have the greatest party blast for their best friend. The next day, he suggests this solution to all his friends leaving out the birthday boy. And guess what, they have managed to surprise the birthday boy with a thunderbolt party bash.

Hence, here also, one can conclude, how the solution to a problem can already exist within one's knowledge. One just needs to put things into perspective and perceive the problem in a more easy way. The properties that we have learned in this tutorial are already used in many of the applications you come across in your daily life, and now, you will be able to better identify the WHY? behind those applications, or maybe, you may just perceive the picture in an unprecedented way.

Abstract

To conclude the article, we started with the introduction of the rectangle where we defined what is rectangular succinctly. Then, we summarized some of the common properties of a rectangle that we use in daily life. Afterwards, we have seen some cool facts about rectangle properties, making one think at least one more time. We then learned a little bit about the rectangle’s history and realized how common a rectangle is in the world that compels one to learn about them. And finally, we have got an even better grip on the rectangle’s properties by helping our friend in the tutorial. I hope these cement your understanding in the domain of measurement. You can learn measurement here as well.