Quadrilateral – Definition, Properties, Types, FAQs, Examples

What is a Quadrilateral?

A quadrilateral is a polygon having four sides, four angles, and four vertices. The word ‘quadrilateral’ is derived from the Latin words ‘quadri,’ which means four, and ‘latus’, which means side.

The above image is an example of a quadrilateral.

Parts of a quadrilateral

1. ∠A, ∠B, ∠C, and ∠D are the four angles of the quadrilateral ABCD
2. AB, BC, CD, and DA are the four sides of the quadrilateral ABCD.
3. A, B, C, and D are the four vertices of the quadrilateral ABCD.
4. AC and BD are the two diagonals of the quadrilateral ABCD.

Non-examples of Quadrilaterals

Shapes that do not have four sides or four angles or have curved sides or are open shapes are non-examples of quadrilaterals.

The above images are some non-examples of quadrilaterals.

Real-life examples of Quadrilaterals

There are many real-life quadrilateral examples: cards, chess boards, traffic signs, etc.

Properties of Quadrilaterals

Some properties are common to all quadrilaterals. These properties are:

• They have four vertices.
• They have four sides.
• The sum of all interior angles is 360°.
• They have two diagonals.
• A quadrilateral can be regular or irregular. A regular quadrilateral must have 4 equal sides, and 4 equal angles, and its diagonals must bisect each other. Square is the only quadrilateral that satisfies all these conditions.

Types of Quadrilaterals

Quadrilaterals can be classified into Parallelograms, Squares, Rectangles, and Rhombuses. Square, Rectangle, and Rhombus are also Parallelograms.

Here’s a list of the types of quadrilaterals with their name, pictures, and properties: 

Concave and Convex Quadrilaterals

Concave quadrilaterals: In concave quadrilaterals, one interior angle is greater than 180°. 

A quadrilateral is called a concave quadrilateral if at least one diagonal, i.e. the line segment joining the vertices is not a part of the same region of the quadrilateral.

Convex quadrilaterals:  In convex quadrilaterals, each interior angle is less than 180°. A quadrilateral is convex if the line segment joining any of its two vertices is in the same region.

Perimeter of Quadrilateral

The perimeter of a quadrilateral is the length of its boundary. This means the perimeter of a quadrilateral equals the sum of all the sides. If ABCD is a quadrilateral then its perimeter will be: AB + BC + CD + DA

Perimeter of quadrilateral ABCD = AB + BC + CD + DA

The formula for the perimeter of some of the common quadrilaterals is given below:

Quadrilateral Name	Perimeter
Rectangle	2 (length + width)
Square	4 x Side
Rhombus	4 x Side
Parallelogram	2 x sum of adjacent sides
Kite	2 x sum of adjacent sides

Area of Quadrilateral

The area of the quadrilateral is the region enclosed by all its sides. The formulas to find out the area of different types of quadrilaterals are shown below:

Solved Examples on Quadrilateral

Example 1. Find the missing angle in the given quadrilateral.

Solution:

We know that the sum of all the angles of a quadrilateral 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 will be the perimeter of a quadrilateral with sides 6 cm, 8 cm, 10 cm, and 12 cm?

Solution:

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

Therefore, perimeter of 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:

In the above example, it is given that –

Area of the Rhombus = 60 square units

Height of the Rhombus = 6 units

Area of rhombus = Base x Height

60 = Base x 6

Base = 60/6 = 10 units

Conclusion

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Practice Problems on Quadrilateral

Frequently Asked Questions on Quadrilateral