In Euclidean geometry, a quadrilateral is a four-sided 2D figure whose sum of internal angles is 360°. The word quadrilateral is acquired from 2 Latin words ‘quadri’ and also ‘latus’ an interpretation four and side respectively. Therefore, identifying the nature of quadrilaterals is essential when do the efforts to distinguish them from various other polygons.

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

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

This is what you’ll review in the article:

Here is a video clip explaining the properties of quadrilaterals:

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

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

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

### Rhombus formulas – area and perimeter of a rhombus

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

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

These practice questions will aid you solidify the nature of rhombus

## Properties that trapezium

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

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

Only one pair of the contrary sides room parallel to each other

### Trapezium formulas – area and also perimeter that a trapezium

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

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

## Properties of quadrilateral – review

The listed below image also summarizes the nature of quadrilaterals

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 every the sides

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Let’s exercise the applications of nature of quadrilateral on the adhering to sample questions:

### GMAT Quadrilaterials exercise Question 1

Adam wants to build a fence roughly his rectangle-shaped garden of length 10 meters and also width 15 meters. How plenty of meters that fence he have to buy to fence the whole garden?

20 meters25 meters30 meters40 meters50 metersSolution

Step 1: Given

Adam has actually a rectangular garden.It has a length of 10 meters and a broad of 15 meters.He wants to develop a fence approximately it.

Step 2: to find

The length compelled to build the fence approximately the entire garden.

Step 3: Approach and also Working out

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

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

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

Therefore, choice E is the correct answer.

### GMAT Quadrilaterials practice Question 2

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

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

Step 1: Given

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

Step 2: come find

The full cost to repaint the wall.

Step 3: Approach and Working out

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

Hence, the correct answer is option E.

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We expect by currently you would have actually learned the different types of quadrilaterals, their properties, and formulas and also how to apply these ideas to solve inquiries on quadrilaterals. The applications of quadrilateral is essential to fix geometry inquiries on the GMAT. If you room planning to take the GMAT, us can assist you through high-quality study product which friend can accessibility for complimentary by registering here.

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Watch this GMAT geometry-free webinar where we discuss how to deal with 700-level Data sufficiency and also Problem inquiries in GMAT Quadrilaterals:

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