In Euclidean geometry, a quadrilateral is a four-sided 2D number whose sum of internal angles is 360°. The word quadrilateral is acquired from 2 Latin indigenous ‘quadri’ and also ‘latus’ definition four and side respectively. Therefore, identifying the properties of quadrilateral is necessary when do the efforts to differentiate them from other polygons.

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

A quadrilateral should be closed form with 4 sidesAll the internal angles of a quadrilateral amount up come 360°

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Here is a video clip explaining the properties of quadrilaterals:

The diagram given below shows a square ABCD and the amount of its interior angles. Every the inner angles amount up to 360°.

Thus, ∠A + ∠B + ∠C + ∠D = 360°      A rhombus is a quadrilateral that has actually the complying with four properties:

Opposite angles space equalAll sides space equal and, the contrary sides space parallel to each otherDiagonals bisect each various other perpendicularlySum of any kind of two surrounding angles is 180°

### Rhombus recipe – area and also perimeter that a rhombus

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

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

## Properties of trapezium

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

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

Only one pair of the contrary sides are parallel to every other

### Trapezium formulas – area and also perimeter of a trapezium

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

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

These exercise questions will aid you solidify the properties of trapezium

## Properties of square – review

The listed below image likewise summarizes the properties of quadrilaterals

The below table summarizes the formulas on the area and perimeter of different varieties 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

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

### GMAT Quadrilaterials practice Question 1

Adam desires to build a fence around his rectangle-shaped garden of size 10 meters and width 15 meters. How plenty of meters of fence he need to buy come 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 a width of 15 meters.He desires to build a fence around it.

Step 2: come find

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

Step 3: Approach and Working out

The fence have the right to only be built roughly the exterior sides the the garden.

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

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

Therefore, option E is the correct answer.

### GMAT Quadrilaterials practice Question 2

Steve desires to paint one rectangular-shaped wall surface of his room. The expense to repaint the wall is \$1.5 every square meter. If the wall is 25 meter long and 18 meter wide, then what is the complete cost to paint the wall?

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

Step 1: Given

Steve wants to repaint one wall surface of his room.The wall surface is 25 meter long and 18 meter wide.Cost to repaint the wall surface is \$1.5 every square meter.

Step 2: to find

The total cost to paint the wall.

Step 3: Approach and Working out

A wall surface is painted across its whole area.So, if we discover the full area the the wall in square meters and also multiply it by the price to paint 1 square meter of the wall then we deserve to the full cost.Area that the wall = size × Breadth = 25 metres × 18 metres = 450 square metreTotal price to paint the wall surface = 450 × \$1.5 = \$675

Hence, the correct answer is alternative E.

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We expect by now you would have actually learned the different species of quadrilaterals, their properties, and formulas and how to use these ideas to solve questions on quadrilaterals. The application of quadrilateral is vital to resolve geometry questions on the GMAT. If you are planning to take it the GMAT, us can assist you with high-quality study product which girlfriend can accessibility for free by registering here.

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