In Euclidean geometry, a square is a four-sided 2D figure whose amount of inner angles is 360°. The word quadrilateral is obtained from 2 Latin native ‘quadri’ and also ‘latus’ definition four and side respectively. Therefore, identify the properties of square is crucial when trying to differentiate them from other polygons.

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

A quadrilateral need to be closed shape with 4 sidesAll the internal angles that a quadrilateral sum up come 360°

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Here is a video clip explaining the nature of quadrilaterals:

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

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

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

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

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

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

These practice questions will aid you solidify the nature of rhombus

## Properties of trapezium

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

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

Only one pair of opposite sides are parallel to every other

### Trapezium recipe – area and perimeter the a trapezium

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

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

These practice questions will assist you solidify the nature of trapezium

## Properties of square – an introduction

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

 Quadrilateral formulas Rectangle Square Parallelogram Rhombus Trapezium Area l × b a² l × h ½× d1 × d2 ½× (Sum the 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 applications of nature of quadrilateral on the complying with sample questions:

### GMAT Quadrilaterials practice Question 1

Adam desires to build a fence approximately his rectangular garden of size 10 meters and also width 15 meters. How many meters the fence he must 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 broad of 15 meters.He wants to build a fence roughly it.

Step 2: to find

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

Step 3: Approach and also Working out

The fence deserve to only be built about the external sides the the garden.

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

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

Therefore, choice E is the exactly answer.

### GMAT Quadrilaterials exercise Question 2

Steve desires to paint one rectangular-shaped wall surface of his room. The cost to repaint the wall surface is \$1.5 every square meter. If the wall is 25 meter long and 18 meter wide, climate what is the full 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 is 25 meters long and also 18 meter wide.Cost to paint the wall is \$1.5 every square meter.

Step 2: to find

The complete cost to paint the wall.

Step 3: Approach and Working out

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

Hence, the exactly answer is alternative E.

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We expect by now you would have actually learned the different types of quadrilaterals, your properties, and formulas and also how to apply these concepts to solve inquiries on quadrilaterals. The applications of quadrilateral is necessary to deal with geometry concerns on the GMAT. If you space planning to take it the GMAT, us can assist you with high-quality study material which you can access for free by registering here.

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Watch this GMAT geometry-free webinar where we talk about how to fix 700-level Data sufficiency and also Problem inquiries in GMAT Quadrilaterals:

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