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 indigenous ‘quadri’ and ‘latus’ definition four and also side respectively. Therefore, identify the nature of quadrilaterals is vital when do the efforts to identify them from other polygons.

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

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

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

Here is a video clip explaining the properties of quadrilaterals:

The chart given listed below shows a quadrilateral ABCD and the amount of its interior angles. Every the interior angles sum up come 360°.

Thus, ∠A + ∠B + ∠C + ∠D = 360°

A rhombus is a quadrilateral that has the complying with four properties:

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

### Rhombus recipe – area and also perimeter the 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 climate the area that a rhombus = ½× d1 × d2

## Properties of trapezium

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

A trapezium is a square in which the following one property:

Only one pair of opposite sides room parallel to every other

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

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

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

## Properties of square – an introduction

The listed below image also summarizes the properties of quadrilaterals

The listed 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 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 application of nature of quadrilaterals on the following sample questions:

### GMAT Quadrilaterials practice Question 1

Adam desires to construct a fence approximately his rectangular garden of size 10 meters and width 15 meters. How numerous meters the fence he have to buy come fence the whole garden?

20 meters25 meters30 meters40 meters50 metersSolution

Step 1: Given

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

Step 2: to find

The length forced to construct the fence approximately the entire garden.

Step 3: Approach and also Working out

The fence can only be built about the external sides the the garden.

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

Hence, the compelled length that 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 expense to repaint the wall surface is \$1.5 per square meter. If the wall is 25 meter long and 18 meters 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 of his room.The wall surface is 25 meters long and 18 meter wide.Cost to paint the wall is \$1.5 per square meter.

Step 2: to find

The complete cost to repaint the wall.

Step 3: Approach and Working out

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

Hence, the exactly answer is choice E.

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We expect by currently you would have actually learned the different species of quadrilaterals, their properties, and formulas and also how to apply these concepts to solve questions on quadrilaterals. The applications of square is essential to deal with geometry questions on the GMAT. If you are planning to take it the GMAT, us can help you v high-quality study product which friend can accessibility for totally free by registering here.

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