In Euclidean geometry, a quadrilateral is a four-sided 2D number whose amount of interior angles is 360°. The word quadrilateral is derived from 2 Latin words ‘quadri’ and also ‘latus’ an interpretation four and also side respectively. Therefore, identify the nature of quadrilaterals is important when do the efforts to identify them from other polygons.

You are watching: Which parallelograms have perpendicular diagonals?

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

A quadrilateral have to be closed shape with 4 sidesAll the inner angles the a quadrilateral sum up to 360°

This is what you’ll read in the article:

Here is a video explaining the properties of quadrilaterals:

The chart given listed below shows a quadrilateral ABCD and also the amount of its internal angles. All the internal angles amount up come 360°.

Thus, ∠A + ∠B + ∠C + ∠D = 360°      Properties the rhombus

A rhombus is a square which has actually the adhering to four properties:

Opposite angles room equalAll sides space equal and, the contrary sides room parallel to each otherDiagonals bisect each other perpendicularlySum of any two nearby angles is 180°Rhombus formulas – Area and perimeter of a rhombus

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

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

These exercise questions will aid you solidify the nature of rhombus

### Trapezium

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

Properties the Trapezium

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

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

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

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

These exercise questions will assist you solidify the properties of trapezium

The below table summarizes all the nature of the quadrilaterals the we have actually learned so far:

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

The listed below image also summarizes the nature of quadrilaterals:

The listed below table summarizes the formulas on the area and also perimeter that different species 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

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

### GMAT Quadrilaterials exercise Question 1

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

20 meters25 meters30 meters40 meters50 metersSolution

Step 1: Given

Adam has a rectangular garden.It has a length of 10 meters and also a width of 15 meters.He desires to develop a fence around it.

Step 2: come find

The length compelled to build the fence roughly the whole garden.

Step 3: Approach and Working out

The fence can only be built approximately the exterior sides the the garden.

So, the complete length of the fence required= sum of lengths of every 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 that the garden.Perimeter = 2 × (10 + 15) = 50 metres

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

Therefore, option E is the exactly answer.

### GMAT Quadrilaterials exercise Question 2

Steve wants to paint one rectangular-shaped wall of his room. The expense to repaint the wall surface is \$1.5 per square meter. If the wall surface is 25 meter long and also 18 meters wide, then what is the full cost to repaint the wall?

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

Step 1: Given

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

Step 2: come find

The complete cost to repaint the wall.

Step 3: Approach and Working out

A wall surface is painted across its whole area.So, if we uncover the total area that the wall in square meters and multiply it by the price to repaint 1 square meter that the wall then we deserve to the total cost.Area that 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 alternative E.

See more: What Is The Smallest Identifiable Unit Of A Compound ? The Smallest Identifiable Unit Of A Compound

We hope by now you would have learned the different varieties of quadrilaterals, their properties, and formulas and how to use these principles to solve questions on quadrilaterals. The applications of square is vital to deal with geometry inquiries on the GMAT. If you space planning to take the GMAT, we can aid you through high-quality study material which you can access for cost-free by registering here.

Here are a few more short articles on Math:

If you space planning to take it the GMAT, us can provide you accessibility to high quality online content to prepare. We space the most the review GMAT prep firm on gmatclub with an ext than 2200+ reviews, as of nine September 2021.