In Euclidean geometry, a quadrilateral is a four-sided 2D figure whose sum of inner angles is 360°. The word quadrilateral is acquired from 2 Latin indigenous ‘quadri’ and ‘latus’ meaning four and also side respectively. Therefore, identify the properties of square is essential when trying to distinguish them from various other polygons.

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So, what are the nature of quadrilaterals?There space two nature of quadrilaterals:

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

In this article, you will obtain an idea around the 5 varieties of quadrilaterals and also get come know about the properties of quadrilaterals.

This is what you’ll read in the article:

Different types of quadrilaterals

Here is a video explaining the properties of quadrilaterals:

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

Thus, ∠A + ∠B + ∠C + ∠D = 360°

Properties the rhombus

A rhombus is a square which has actually the complying with four properties:

Opposite angles room equalAll sides space equal and, opposite sides are parallel to every otherDiagonals bisect each various other perpendicularlySum of any kind of two nearby angles is 180°Rhombus formulas – Area and also perimeter of a rhombus

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

If the size of 2 diagonals the the rhombus is d1 and d2 then the area the a rhombus = ½× d1 × d2

These practice questions will help you solidify the properties of rhombus

### Trapezium

A trapezium (called Trapezoid in the US) is a square that has only one pair that parallel sides. The parallel political parties are described as ‘bases’ and the other two political parties are called ‘legs’ or lateral sides.

Properties of Trapezium

A trapezium is a quadrilateral in i beg your pardon the complying with one property:

Only one pair of the opposite sides space parallel to every otherTrapezium formulas – Area and perimeter the a trapezium

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

Perimeter the the trapezium= amount of lengths of every the political parties = ab + BC + CD + DAArea of the trapezium =½ × (Sum the lengths of parallel sides) × h = ½ × (AB + CD) × h

These practice questions will help you solidify the nature of trapezium

## Properties that quadrilaterals

The below table summarizes every the properties of the quadrilaterals that we have learned therefore far:

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

The listed below image also summarizes the nature of quadrilaterals:

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

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

## Quadrilateral practice Question

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

### GMAT Quadrilaterials exercise Question 1

Adam desires to build a fence roughly his rectangle-shaped garden of length 10 meters and width 15 meters. How plenty of meters of fence he need to buy to fence the entire garden?

20 meters25 meters30 meters40 meters50 metersSolution

Step 1: Given

Adam has actually a rectangular garden.It has a length of 10 meters and also a broad of 15 meters.He desires to construct a fence about it.

Step 2: to find

The length compelled to construct the fence around the entire garden.

Step 3: Approach and also Working out

The fence deserve to only it is in built about the external sides of the garden.

So, the full length that the fence required= sum of lengths of all the political parties of the garden.Since the garden is rectangular, the sum of the length of every the sides is nothing yet the perimeter the the garden.Perimeter = 2 × (10 + 15) = 50 metres

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

Therefore, alternative E is the exactly answer.

### GMAT Quadrilaterials practice Question 2

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

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

Step 1: Given

Steve desires to repaint one wall surface of his room.The wall surface is 25 meters long and also 18 meters wide.Cost to paint the wall surface 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 whole area.So, if we find the complete area that the wall surface in square meters and multiply it by the price to paint 1 square meter that the wall then we can the total cost.Area the the wall surface = length × Breadth = 25 metres × 18 metres = 450 square metreTotal expense to repaint the wall surface = 450 × \$1.5 = \$675

Hence, the correct answer is option E.

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We hope by currently you would have actually learned the different varieties of quadrilaterals, their properties, and formulas and also how to apply these ideas to solve concerns on quadrilaterals. The applications of square is crucial to resolve geometry questions on the GMAT. If you room planning to take the GMAT, we can help you v high-quality study material which you can access for free by registering here.

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