Properties of Rectangle: Definition, Formulas, Problems

Properties of Rectangle: We see many rectangular objects in our day-to-day lives. But do we know what is a rectangle? or what are the properties of rectangles? A rectangle is a plane, a geometrical figure. It is also a quadrilateral with all four equal angles and whose opposite sides are equal and parallel.

Two dimensions – length and width, usually characterise a rectangle. The longer side of a rectangle is called length, while the shorter side is called width. In this article, students will learn everything about a rectangle, such as its definition, diagram, properties, and solve examples related to the properties of a rectangle.

Rectangle Properties: What is a Rectangle?

The word rectangle comes from the Latin word rectangular, which comes from two words – rectus, meaning ‘right’ or ‘proper’ and angulus, meaning angle. As students can guess from the name, a rectangle comprises right angles. To get a clear idea, let us look at the definition of a rectangle.

A rectangle is a two-dimensional geometrical shape that has four sides, four vertices, and four angles. The opposite sides of a rectangle are equal in length and parallel to each other. Also, each of the four internal angles of a rectangle measures 90°.

Note that a rectangle is a quadrilateral. Some other types of quadrilaterals are:

a. Square
b. Parallelogram
c. Kite
d. Rhombus
e. Trapezoid

When it comes to solving questions related to the properties of rectangles, rhombuses and squares it is easier to deal with than the rest of the quadrilaterals.

Properties of Rectangle: What are the Properties of Rectangles?

Let us now look into some of the basic rectangle properties:

• A rectangle is a quadrilateral with four equal internal angles.
• Each internal angle of a rectangle measures 90°.
• As the opposite angles of a rectangle are equal, a rectangle is also a parallelogram.
• The opposite sides of a rectangle are equal and parallel.
• The diagonals of a rectangle bisect each other and are of the same length.
• The two diagonals of a rectangle bisect each other at different angles – one obtuse angle and the other an acute angle.
• A rectangle whose two diagonals bisect each other at right angles is called a square.
• As the two equal diagonals of a rectangle bisect each other, the four vertices of a rectangle are equidistant from the point of bisection. This means a circumcircle can be formed with its centre at the point of bisection of the diagonals and its circumference passing through the four vertices of the rectangle. The diameter of the circumcircle is equal to the diagonal of the rectangle.

Formulas of Rectangle

Some of the important rectangle formulas are as under:

i. Area of a Rectangle, A = a × b, where a and b are the length and the breadth of the rectangle, respectively. That is:

ii. Perimeter of a Rectangle, S = Total length of all sides of the rectangle = 2 (a + b).

iii. Each of the diagonals of a rectangle divides the rectangle into two right-angled triangles with the diagonal being the hypotenuse.

As per Pythagoras’ Theorem, the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides.

So, we have, (Diagonal)² = (Length)² + (Breadth)².

From this,

Practice 10th CBSE Exam Questions

Problems with Properties of a Rectangle

Students can practice the properties of rectangles worksheet:

Example 1: If the length and the breadth of a rectangle are 8 cm and 5 cm respectively, find its area and perimeter.

Solution:

Here, length of the rectangle, a = 8 cm
Breadth of the rectangle, b = 5 cm.

Therefore, area = Length (a) × Breadth (b) = (8 × 5) cm² = 40 cm².
Perimeter = 2 (Length + Breadth) = 2 (8 + 5) = 2 × 13 = 26 cm.

Example 2: If the breadth and diagonal of a rectangle are 6 cm and 10 cm respectively, find its breadth.

Solution:

Here, breadth of the rectangle, b = 6 cm
Diagonal of the rectangle, D = 10 cm

We know that, (Diagonal)² = (Length)² + (Breadth)².

Therefore, we have,
10² = a² + 6²
=> a² = 10² – 6² = 100 – 36 = 64
=> a = √64 = 8 cm.

So, now you know the properties of rectangles. Solve more questions of varying types and master the topic. You can also check out the properties of rectangle worksheet pdf.

Strong command over elementary mathematics is important for everyone as basic numerical ability is important not only for school-level Maths exams but also for various competitive exams like CAT, MAT, and exams for government job recruitment. Also, these simple concepts lay the foundation required to understand complex concepts in higher classes. So, students must take the subject seriously from the early classes.

You can also check,

Frequently Asked Questions Related to Properties of Rectangle

Some of the frequently asked questions about the properties of rectangles and their answers are as under:

Q1. How is the area of a rectangle calculated?
Ans. The area of a rectangle is calculated by multiplying its length by its breadth.

Q2. What is the difference between a rectangle and a square?
Ans. Both rectangle and square are closed geometrical figures with four sides and four internal angles (each angle measuring 90 degrees). The four sides of a square are equal. Whereas, in a rectangle, the adjacent sides have different lengths. The opposite sides are equal.

Q3. What is the basis of a rectangle?
Ans. The rectangle or square helps get measurements like a house, building measurements, and many other useful everyday objects rectangular or square. Buildings are rectangular, mainly due to straight walls and floors having built-in depth.

Q4. What are the 5 properties of a rectangle?
Ans. The 5 properties of a rectangle are as follows:
1. A rectangle is a quadrilateral.
2. The opposite sides are equal to each other and parallel
3. The interior angle is equal to 90 degrees.
4. The sum of all the interior angles is equal to 360 degrees.
5. The diagonals bisect each other and have the same length.

Q5. What do all rectangles have in common?
Ans. A rectangle is a 2-dimensional shape having four sides and four corners. Its two sides meet at right angles. Therefore, the opposite sides of a rectangle have the same lengths and are parallel.

Q6. Is a rectangle a parallelogram?
Ans. Yes, a rectangle is a parallelogram as pairs of opposite sides are parallel. Since a rectangle also has a unique characteristic, all angles are right angles; all four angles are corresponding.

We hope this article on the Properties of rectangles helps you. If you have any queries, feel to ask in the comment section below. We will get back to you at the earliest.

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