**Table of Contents**

**What are the Properties Of Rectangle?**

We can identify a rectangle at a glance thanks to its unique properties. An object with two dimensions that has four sides, four vertices, and four angles is called a rectangle. A rectangle has two sides that are equal in length and parallel to one another. In addition, because a rectangle has four identical angles, the angles created by its adjacent sides are always 90°. It’s important to remember that while a rectangle’s sides aren’t always equal, its opposites are almost always congruent.

Rectangles are frequently found in everyday objects, including kites, paintings, slabs, storage boxes, and many other things.

Examine the rectangle shown above and relate it to the following properties of a rectangle to gain a better knowledge of the rectangle:

- A quadrilateral with four congruent internal angles is a rectangle.
- A rectangle’s opposite sides are parallel and of equal length.

- In a rectangle, each vertex is 90° in angle.
- The total of a rectangle’s internal angles is 360°.
- A rectangle’s diagonals cut each other in half.
- The diagonals are equal in length.
- The length of the diagonals can be determined using the Pythagorean Theorem. The length of the diagonal with sides ‘a’ and ‘b’ is (a2 + b2).
- A rectangle is also referred to as a parallelogram because of the parallelism of its sides.

**Formulas of a Rectangle**

It’s crucial to keep in mind three fundamental formulas in order to work with rectangles efficiently. The area, perimeter, and diagonal length of the rectangle are determined using these formulas.

The formula for calculating a rectangle’s area is A = l w, where l is the rectangle’s length and w is its width.

P = 2(l + w), where ‘l’ and ‘w’ stand for the length and width of the rectangle, respectively, will give you the perimeter of a rectangle.

The Pythagorean theorem can also be used to determine the length of a rectangle’s diagonal, d: d = (l2 + w2), where l and w are the rectangle’s length and width, respectively.

**Types of Rectangles**

A rectangle is defined as having four equal sides with neighbouring sides coming together at a 90° angle. The Square and the Golden Rectangle, two different forms of rectangles, both exhibit these distinguishing characteristics

**Square:** A specific variety of rectangle known as a “square” has four equal sides and angles. There are also 90° internal angles at each vertex of this two-dimensional form. A square also has equal and parallel opposite sides, and its diagonals cross at a 90-degree angle. It’s interesting to notice that while not all rectangles can be squares, all squares are regarded to be rectangles.

**Golden Rectangle:**

The Golden Rectangle is a rectangle whose sides are proportionate to the golden ratio, which can be written as (a + b)/a = a/b, where ‘a’ stands for the rectangle’s width and (a + b) for its length. In particular, a Golden Rectangle’s length-to-width ratio is very near to the golden ratio, which is 1:(1+5)/2. For instance, the width of a Golden Rectangle will be roughly 1.168 feet long (or vice versa) if the length is roughly 1 foot, where the Golden Ratio is equal to 1:1.618.

The Golden Rectangle and its associated length and width are shown in the accompanying figure.

**Area and Perimeter of a Rectangle?**

The amount of space a rectangle takes up is referred to as its area. The rectangle’s length and breadth can be multiplied to find it. So, the following is the formula to determine a rectangle’s area:

The length and width of a rectangle are multiplied to find its area, which is typically expressed in square units like square metres (m2) or square inches (in2).

On the other hand, a rectangle’s perimeter equals the sum of all of its sides. Simply adding the lengths of all four sides yields the formula for a rectangle’s perimeter, which is:

**Rectangle perimeter: length + width + length + width**

= 2 × length + 2 × width

= 2 (length + width)

**Solved Problems:**

**Question 1**

**Determine the perimeter of a rectangle whose sides are, respectively, 50 cm and 25 cm.**

**Solution**

a = 50 cm

b = 25 cm

The perimeter of a rectangle is as follows based on a rectangle’s properties:

perimeter with units of 2a + 2b

P = 2 (a + b) units.

Substitute the values now.

P = 2(50+25)

P = 2(75)

P = 150 cm

**Question 2**

**What is the area and length of the diagonal of a rectangle with adjacent side lengths of 35 cm and 12 cm?**

**Solution:**

Let the measures of adjacent sides of a rectangle be:

a = 35 cm

b = 12 cm

As we know,

Area of a rectangle = ab

= 35 × 12

= 420 cm2

Therefore, the area of a rectangle is 420 cm2.

**Frequently Asked Questions – FAQs**

**What is the length property of a parallelogram?**

The length property of a parallelogram states that the opposite sides of a parallelogram are parallel and equal in length.

**What is the sum of all interior angles of a square?**

The sum of all interior angles of a square is 360 degrees.

**Do the diagonals of a parallelogram have equal lengths?**

No, the diagonals of a parallelogram do not necessarily have equal lengths.