In Euclidean geometry, a square is a four-sided 2D number whose sum of internal angles is 360°. Words quadrilateral is derived from two Latin native ‘quadri’ and ‘latus’ definition four and also side respectively. Therefore, identifying the nature of quadrilaterals is important when make the efforts to distinguish them from various other polygons.

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

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

This is what you’ll review in the article:

Here is a video explaining the properties of quadrilaterals:

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

Thus, ∠A + ∠B + ∠C + ∠D = 360°

Properties of rhombus

A rhombus is a square which has actually the following 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 type of two adjacent angles is 180°Rhombus recipe – Area and also perimeter of a rhombus

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

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

### Trapezium

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

Properties that Trapezium

A trapezium is a square in i m sorry the following one property:

Only one pair of the contrary sides are parallel to every otherTrapezium formulas – Area and perimeter that a trapezium

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

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

The listed below table summarizes all the nature of the quadrilaterals that we have learned for this reason far:

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

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 the parallel sides) × height Perimeter 2 × (l + b) 4a 2 × (l + b) 4a Sum of all the sides

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

### GMAT Quadrilaterials practice Question 1

Adam desires to build a fence about his rectangle-shaped garden of length 10 meters and width 15 meters. How plenty of meters the 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 actually a length of 10 meters and a broad of 15 meters.He wants to develop a fence around it.

Step 2: come find

The length forced to develop the fence about the entire garden.

Step 3: Approach and Working out

The fence can only it is in built approximately the outside sides that the garden.

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

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

Therefore, alternative E is the correct answer.

### GMAT Quadrilaterials practice Question 2

Steve desires to repaint 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, then what is the total cost to repaint 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 repaint the wall is \$1.5 per square meter.

Step 2: to find

The total cost to repaint the wall.

Step 3: Approach and also Working out

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

Hence, the correct answer is alternative E.

See more: Representation Of A Substance Using Symbols, Writing Chemical Equations

We hope by now you would have learned the different varieties of quadrilaterals, their properties, and also formulas and also how to apply these principles to solve inquiries on quadrilaterals. The application of square is necessary to fix geometry questions on the GMAT. If you space planning to take the GMAT, us can help you with high-quality study product which you can access for free by registering here.

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