In Euclidean geometry, a quadrilateral is a four-sided 2D figure whose amount of internal angles is 360°. The word quadrilateral is obtained from two Latin words ‘quadri’ and ‘latus’ meaning four and also side respectively. Therefore, identify the nature of quadrilaterals is necessary when trying to identify them from various other polygons.

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

A quadrilateral should be closed shape with 4 sidesAll the interior angles that a quadrilateral amount up to 360°

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

This is what you’ll check out in the article:

Here is a video explaining the nature of quadrilaterals:

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

Thus, ∠A + ∠B + ∠C + ∠D = 360°

Properties the rhombus

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

Opposite angles are equalAll sides are equal and, opposite sides are parallel to every otherDiagonals bisect each other perpendicularlySum of any kind of two surrounding angles is 180°Rhombus recipe – Area and also perimeter that 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 climate the area of a rhombus = ½× d1 × d2

### Trapezium

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

Properties that Trapezium

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

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

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

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

These practice questions will aid you solidify the properties of trapezium

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

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

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

Let’s practice the applications of nature of quadrilateral on the complying with sample questions:

### GMAT Quadrilaterials exercise Question 1

Adam wants to build a fence around his rectangle-shaped garden of length 10 meters and also width 15 meters. How countless meters of fence he need to buy come fence the entire garden?

20 meters25 meters30 meters40 meters50 metersSolution

Step 1: Given

Adam has a rectangle-shaped garden.It has actually a size of 10 meters and also a width of 15 meters.He desires to construct a fence roughly it.

Step 2: to find

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

Step 3: Approach and also Working out

The fence deserve to only be built approximately the exterior sides that the garden.

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

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

Therefore, option 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 paint the wall is \$1.5 per square meter. If the wall is 25 meters long and 18 meter wide, then what is the complete cost to paint 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 meter long and also 18 meter wide.Cost to paint the wall is \$1.5 every square meter.

Step 2: come 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 discover the complete area of the wall surface in square meters and multiply the by the price to repaint 1 square meter the the wall then we deserve to the complete cost.Area the the wall surface = length × Breadth = 25 metres × 18 metres = 450 square metreTotal price to repaint the wall = 450 × \$1.5 = \$675

Hence, the exactly answer is option E.

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We expect by currently you would have learned the different species of quadrilaterals, their properties, and formulas and also how to apply these ideas to solve inquiries on quadrilaterals. The application of quadrilateral is essential to solve geometry inquiries on the GMAT. If you room planning to take it the GMAT, us can aid you v high-quality study material which friend can access for complimentary by registering here.