Properties Of Rectangle: If you are looking for Properties of Rectangle, you have come to the right place. In this article, we will provide you with the definition, diagram, properties, formulas, and examples related to Rectangle.
Rectangle is a plane, geometrical figure that is a common appearance in our day-to-day life and finds importance in geometry and mensuration. It is, therefore, important for students to be aware of its definition and properties. Read this article and know everything important about Rectangle.
Properties Of Rectangle
The word rectangle comes from the Latin word rectangulus, which is again derived from two words – rectus, meaning right or proper and angulus, meaning angle.
As you can assume from the name itself, a rectangle comprises right angles. To get a clear idea, let’s look at the definition of a rectangle.
What Is 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:
When it comes to solving questions related to quadrilaterals, squares and rectangles are easier to deal with than the rest of the others.
Properties Of Rectangle
Let us now look into some of the basic rectangle properties:
a. A rectangle is a quadrilateral with four equal internal angles.
b. Each internal angle of a rectangle measures 90°.
c. As the opposite angles of a rectangle are equal, a rectangle is also a parallelogram.
d. The opposite sides of a rectangle are equal and parallel.
e. The diagonals of a rectangle bisect each other and are of the same length.
f. The two diagonals of a rectangle bisect each other at different angles – one obtuse angle and the other an acute angle.
g. A rectangle whose two diagonals bisect each other at right angles is called a square.
h. 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 center 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:
|Area of a Rectangle = Length (a) × Breadth (b)|
ii. Perimeter of a Rectangle, S = Total length of all sides of the rectangle = 2 (a + b).
|Perimeter of a Rectangle = 2 (Length + Breadth) = 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.
|Length of Diagonal (D) = √[(Length)2 + (Breadth)2] = √(a2 + b2)|
Problems On Rectangle
Here are a few example problems on rectangles:
Example 1: If the length and the breadth of a rectangle are 8 cm and 5 cm respectively, find its area and perimeter.
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.
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 rectangle. Solve more questions of varying type and master the topic.
Other Articles On Maths
Some other helpful Maths articles by Embibe are provided below:
|HCF And LCM|
|Properties Of Triangles|
|Properties Of Circle|
Strong command over elementary mathematics is important for everyone as a basic numerical ability is important for 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.
At Embibe, we provide free Maths practice questions for Class 8, 9, 10, 11, and 12 along with detailed solutions:
|a. Class 8 Maths Practice Questions|
|b. Class 9 Maths Practice Questions|
|c. Class 10 Maths Practice Questions|
|d. Class 11-12 Maths Practice Questions|
So, make the best use of these resources and master the subject.
We hope this article on Properties of Rectangle helps you. If you have any queries, feel free to ask in the comment section below. We will get back to you at the earliest.637 Views