Types of Rectangles and Their Importance in CAT Exams

The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.

Definition:

A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.

Important Properties of a Rectangle:

The rectangle’s characteristics are listed below:

1. There are exactly 90 degrees in each internal angle.

2. A rectangle’s diagonals cut each other in half.

3. A rectangle’s opposite sides are parallel to one another.

4. 360 degrees is the total of all interior angles.

5. The four external angles add up to a 360-degree angle.

6. The length of both diagonals is the same.

7. A rectangle’s area can be calculated by multiplying the length by the breadth or vice versa. Area: a*b

8. 2*(a+b) is the perimeter of a rectangle.

9. The diagonal length of a rectangle is (a² + b²)1/2.

10. A rectangle’s diagonals cut across one another at various angles. There are two angles: one is acute, the other obtuse. Observation: A rectangle is said to be square if its two diagonals meet at a 90-degree angle.

11. It exhibits rotational symmetry of order 2 (through 180°) and two lines of reflectional symmetry.

Characteristics of a Rectangle:

The dimensions of a rectangle are its length (L) and width (W) . Different scales are used for the length and the width. As seen in the diagram, a rectangle ABCD has four sides: AB, BC, CD, and DA, as well as the right angles: A, B, C, and D. The given rectangle is defined as having a width (W) equal to the distance between B and C or A and D and a length (L) equal to the distance between A and B or C and D.

Types of Rectangles:

A rectangle has four equal sides, with the neighbouring sides meeting at a 90° angle on each side. Both the Square Rectangle and the Golden Rectangle exhibit these characteristics.

Square Rectangle

An example of a rectangle is a square, which has four equal sides and four equal angles. The inner angles at each vertex of this two-dimensional form are 90 degrees. Along with these characteristics, a square also has equal and parallel opposing sides and diagonals that are 90 degrees apart. While all rectangles cannot be squares, all squares can be claimed to be rectangles.

Golden Rectangle 

The golden rectangle is a shape whose sides have the golden ratio, or (a + b)/a = a/b, where “a” denotes the rectangle’s width and (a + b) its length. A golden rectangle is, in other words, a rectangle whose “length to width ratio” is close to the golden ratio, which is 1: (1+ 5)/2. The Golden Ratio is 1:1.618, therefore if the length is approximately 1 foot long, the width will be 1.168 feet long, and vice versa. Look at the accompanying illustration, which displays the dimensions of the golden rectangle.

Rectangular Formulas

There are three essential rectangular formulas that must be retained. They have something to do with a rectangle’s surface area, outline, and diagonal length.

1. The formula for calculating a rectangle’s area is A = l × w, where l and w stand for the rectangle’s length and breadth, respectively.

2. The formula for a rectangle’s perimeter is P = 2(l + w), where l stands for the rectangle’s length and w for its width.

3. The diagonal of a rectangle (d) is equal to √(l² + w²), where l is the rectangle’s length and w is its width. The Pythagoras theorem is the source of the formula for a rectangle’s diagonal.

Conclusion

To sum up the essay, we began with an explanation of the rectangle and provided a brief definition of what a rectangle is. Then, we enumerated a few of the typical characteristics of a rectangle that we encounter every day. After that, we learned some interesting information about the characteristics of rectangles, which made us pause to consider something else. The history of the rectangle was then briefly discussed, and we came to understand how ubiquitous rectangles are in daily life. Finally, through assisting our friend in the tutorial, we have a stronger understanding of the properties of the rectangle. I hope these solidify your knowledge of the measurement field. Here, you can also learn about measuring.