In Euclidean geometry, a quadrilateral is a four-sided 2D figure whose sum of internal angles is 360°. The word quadrilateral is derived from two Latin words ‘quadri’ and ‘latus’ meaning four and side respectively. Therefore, identifying the properties of quadrilaterals is important when trying to distinguish them from other polygons.

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So, what are the properties of quadrilaterals?There are two properties of quadrilaterals:

A quadrilateral should be closed shape with 4 sidesAll the internal angles of a quadrilateral sum up to 360°

This is what you’ll read in the article:

Here is a video explaining the properties of quadrilaterals:

The diagram given below shows a quadrilateral ABCD and the sum of its internal angles. All the internal angles sum up to 360°.

Thus, ∠A + ∠B + ∠C + ∠D = 360°      Properties of rhombus

A rhombus is a quadrilateral which has the following four properties:

Opposite angles are equalAll sides are equal and, opposite sides are parallel to each otherDiagonals bisect each other perpendicularlySum of any two adjacent angles is 180°Rhombus formulas – Area and perimeter of a rhombus

If the side of a rhombus is a then, perimeter of a rhombus = 4a

If the length of two diagonals of the rhombus is d1 and d2 then the area of a rhombus = ½× d1 × d2

### Trapezium

A trapezium (called Trapezoid in the US) is a quadrilateral that has only one pair of parallel sides. The parallel sides are referred to as ‘bases’ and the other two sides are called ‘legs’ or lateral sides.

Properties of Trapezium

A trapezium is a quadrilateral in which the following one property:

Only one pair of opposite sides are parallel to each otherTrapezium formulas – Area and perimeter of a trapezium

If the height of a trapezium is ‘h’(as shown in the above diagram) then:

Perimeter of the trapezium= Sum of lengths of all the sides = AB + BC + CD + DAArea of the trapezium =½ × (Sum of lengths of parallel sides) × h = ½ × (AB + CD) × h

The below table summarizes all the properties of the quadrilaterals that we have learned so far:

 Properties of quadrilaterals Rectangle Square Parallelogram Rhombus Trapezium All Sides are equal ✖ ✔ ✖ ✔ ✖ Opposite Sides are equal ✔ ✔ ✔ ✔ ✖ Opposite Sides are parallel ✔ ✔ ✔ ✔ ✔ All angles are equal ✔ ✔ ✖ ✖ ✖ Opposite angles are equal ✔ ✔ ✔ ✔ ✖ Sum of two adjacent angles is 180 ✔ ✔ ✔ ✔ ✖ Bisect each other ✔ ✔ ✔ ✔ ✖ Bisect perpendicularly ✖ ✔ ✖ ✔ ✖

The below image also summarizes the properties of quadrilaterals:

The below table summarizes the formulas on the area and perimeter of different types of quadrilaterals:

 Quadrilateral formulas Rectangle Square Parallelogram Rhombus Trapezium Area l × b a² l × h ½× d1 × d2 ½× (Sum of parallel sides) × height Perimeter 2 × (l + b) 4a 2 × (l + b) 4a Sum of all the sides

Let’s practice the application of properties of quadrilaterals on the following sample questions:

### GMAT Quadrilaterials Practice Question 1

Adam wants to build a fence around his rectangular garden of length 10 meters and width 15 meters. How many meters of fence he should buy to fence the entire garden?

20 meters25 meters30 meters40 meters50 metersSolution

Step 1: Given

Adam has a rectangular garden.It has a length of 10 meters and a width of 15 meters.He wants to build a fence around it.

Step 2: To find

The length required to build the fence around the entire garden.

Step 3: Approach and Working out

The fence can only be built around the outside sides of the garden.

So, the total length of the fence required= Sum of lengths of all the sides of the garden.Since the garden is rectangular, the sum of the length of all the sides is nothing but the perimeter of the garden.Perimeter = 2 × (10 + 15) = 50 metres

Hence, the required length of the fence is 50 meters.

Therefore, option E is the correct answer.

### GMAT Quadrilaterials Practice Question 2

Steve wants to paint one rectangular-shaped wall of his room. The cost to paint the wall is \$1.5 per square meter. If the wall is 25 meters long and 18 meters wide, then what is the total cost to paint the wall?

\$ 300\$ 350\$ 450\$ 600\$ 675Solution

Step 1: Given

Steve wants to paint one wall of his room.The wall is 25 meters long and 18 meters wide.Cost to paint the wall is \$1.5 per square meter.

Step 2: To find

The total cost to paint the wall.

Step 3: Approach and Working out

A wall is painted across its entire area.So, if we find the total area of the wall in square meters and multiply it by the cost to paint 1 square meter of the wall then we can the total cost.Area of the wall = length × Breadth = 25 metres × 18 metres = 450 square metreTotal cost to paint the wall = 450 × \$1.5 = \$675

Hence, the correct answer is option E.

See more: What Does Robles Mean In English, Roble Meaning

We hope by now you would have learned the different types of quadrilaterals, their properties, and formulas and how to apply these concepts to solve questions on quadrilaterals. The application of quadrilaterals is important to solve geometry questions on the GMAT. If you are planning to take the GMAT, we can help you with high-quality study material which you can access for free by registering here.

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