In Euclidean geomeattempt, a quadrilateral is a four-sided 2D number whose amount of interior angles is 360°. The word quadrilateral is acquired from 2 Latin words ‘quadri’ and ‘latus’ meaning 4 and also side respectively. Thus, identifying the properties of quadrilaterals is crucial as soon as trying to differentiate them from various other polygons.

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So, what are the properties of quadrilaterals?Tbelow are two properties of quadrilaterals:

A quadrilateral need to be closed form with 4 sidesAll the interior angles of a quadrilateral amount as much as 360°

This is what you’ll read in the article:

Here is a video explaining the properties of quadrilaterals:

The diagram offered below shows a quadrilateral ABCD and the amount of its internal angles. All the internal angles amount as much as 360°.

Therefore, ∠A + ∠B + ∠C + ∠D = 360°      Properties of rhombus

A rhombus is a quadrilateral which has the adhering to 4 properties:

Opposite angles are equalAll sides are equal and also, oppowebsite sides are parallel to each otherDiagonals bisect each various other perpendicularlySum of any type of 2 adjacent angles is 180°Rhombus formulas – Area and also perimeter of a rhombus

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

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

These exercise concerns will certainly help you solidify the properties of rhombus

### Trapezium

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

Properties of Trapezium

A trapezium is a quadrilateral in which the adhering to one property:

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

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

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

These practice questions will aid you solidify the properties of trapezium

The listed below table summarizes all the properties of the quadrilaterals that we have learned so far:

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

The listed below picture also summarizes the properties of quadrilaterals:

The below table summarizes the formulas on the location and also perimeter of various kinds of quadrilaterals:

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

Let’s practice the application of properties of quadrilaterals on the adhering to sample questions:

### GMAT Quadrilaterials Practice Inquiry 1

Adam wants to develop a fence roughly his rectangular garden of size 10 meters and width 15 meters. How many type of meters of fence he need to buy to fence the whole garden?

20 meters25 meters30 meters40 meters50 metersSolution

Tip 1: Given

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

Step 2: To find

The size forced to construct the fence around the entire garden.

Tip 3: Approach and also Working out

The fence deserve to just be built about the exterior sides of the garden.

So, the complete length of the fence required= Sum of lengths of all the sides of the garden.Due to the fact that the garden is rectangular, the sum of the length of all the sides is nothing yet the perimeter of the garden.Perimeter = 2 × (10 + 15) = 50 metres

Hence, the compelled size of the fence is 50 meters.

Therefore, alternative E is the correct answer.

### GMAT Quadrilaterials Practice Question 2

Steve wants to paint one rectangular-shaped wall of his room. The price to paint the wall is \$1.5 per square meter. If the wall is 25 meters lengthy and also 18 meters wide, then what is the complete price to paint the wall?

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

Step 1: Given

Steve wants to paint one wall of his room.The wall is 25 meters long and 18 meters wide.Cost to paint the wall is \$1.5 per square meter.

Step 2: To find

The complete price to paint the wall.

Step 3: Approach and also Working out

A wall is painted across its entire location.So, if we find the complete area of the wall in square meters and multiply it by the cost to paint 1 square meter of the wall then we have the right to the full cost.Area of the wall = size × Breadth = 25 metres × 18 metres = 450 square metreTotal cost to paint the wall = 450 × \$1.5 = \$675

Hence, the correct answer is choice E.

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We hope by now you would have actually learned the various kinds of quadrilaterals, their properties, and formulas and just how to apply these concepts to resolve inquiries on quadrilaterals. The application of quadrilaterals is necessary to resolve geometry inquiries on the GMAT. If you are planning to take the GMAT, we have the right to help you with high-high quality research product which you can access for cost-free by registering here.