A quadrilateral always has four angles, four sides, and four vertices. However, the measure of the sides and angles can differ. Therefore, a quadrilateral can be of different kinds.

• Parallelogram: It is a quadrilateral with equal and parallel opposite sides. Therefore, the opposite angles of a parallelogram are also equal.

• Rectangle: It is a quadrilateral with equal and parallel opposite sides. All its angles measure 90°.

• Rhombus: It is a quadrilateral with four equal sides and angles.

• Square: It is a quadrilateral with four equal sides. All its angles measure 90°.

• Trapezium: It is a quadrilateral with only one pair of parallel sides.

What are concave and convex quadrilaterals?

• Concave quadrilaterals: In concave quadrilaterals, one interior angle is greater than 180°.
• Convex Quadrilaterals: In convex quadrilaterals, each interior angle is less than 180°.

Below are the examples of concave and convex quadrilaterals:

Irregular Quadrilaterals: Quadrilaterals with four equal sides and angles are called a square. Apart from that, all the other quadrilaterals are irregular.

Complex Quadrilaterals: When two sides cross over in a quadrilateral, it is called a self-intersecting or complex quadrilateral. The examples of complex quadrilaterals are:

A quadrilateral’s perimeter is the length of its boundary. This means the perimeter of a quadrilateral equals the sum of all four sides. For example, suppose ABCD is a quadrilateral, its perimeter will be BC + CD + DA + AB.

Quadrilateral Name	Perimeter Formula
Rectangle	2(Length + Width)
Square	4 ✕ Side
Rhombus	4 ✕ Side
Parallelogram	2 ✕ sum of adjacent sides

 

The area of a quadrilateral is the region enclosed by all its sides. The formula to find the area of different types of quadrilaterals is as below:

Important facts about quadrilaterals:

• A quadrilateral can be called a trapezium or trapezoid when it has two sides that are parallel to each other.
• A quadrilateral can be called a parallelogram when it has two sides that are parallel to each other.
• A quadrilateral can be called a rhombus when all four sides are of equal length. And the two pairs are parallel to each other. 

Solved Examples

Example 1. Which is the missing angle of the given quadrilateral.

Solution:

We know that the sum of a quadrilateral’s angles is 360°.

Hence, we can write it as follows:

 x + 77° + 101°  + 67° = 360°

x  +  245°  =  360°

x = 360° – 245°

Therefore,  x =  115°

Example 2: What is the perimeter of a quadrilateral with sides 6 cm, 8 cm, 10 cm, and 12 cm?

Solution:

Given, sides of a quadrilateral are 6 cm, 8 cm, 10 cm, and 12 cm.

Therefore, the perimeter of the quadrilateral is:

P =  6 cm + 8 cm + 10 cm + 12 cm = 36 cm

Example 3: If the area of a rhombus is 60 square units and its height is 6 units, what will be the value of its base?

Solution:

Given:

Area of the rhombus = 60 square units

Height of the rhombus = 6 units

Area of rhombus = Base ✕ Height

60 = Base ✕ 6

Base = 60/6 = 10 units

Practice Problems

1. Which type of quadrilateral has all the angles measuring 90° and equal opposite sides?

a) Rectangle

b) Parallelogram

c) Square

d) None of the above

Ans. a) Rectangle

2. How many sides are there in a quadrilateral?

a) 3

b) 2

c) 4

d) 1

Ans. c) 4

3. What is the sum of the interior angles of a quadrilateral?

a) 120°

b) 360°

c) 520°

d) None of these

Ans. b) 360°

Class 9 mathematics chapters, especially the quadrilateral chapter, is important for students to learn application-based mathematics. Practising more quadrilateral questions will help students develop analytical skills and solve these problems quickly. It will also increase their score in the examination. This guide has taught us that a quadrilateral is a closed polygon with four sides, four angles, and four verticals. 

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1. How many vertices does a quadrilateral have?

Ans. A quadrilateral has four vertices.

2. Can we say that a parallelogram is a quadrilateral?

Ans. Yes, a parallelogram is a closed figure with four angles. Hence, it can be called a quadrilateral.

3. What is the name of the quadrilateral that has all angles measuring 90°, and equal opposite sides?

Ans. Rectangle.

4. Are all the angles of a quadrilateral acute?

Ans. No, all the angles of a quadrilateral cannot be acute because then the sum of angles of the quadrilateral will be less than 360°.