In Euclidean geometry, a quadrilateral is a four-sided 2D number whose sum of inner angles is 360°. Words quadrilateral is derived from two Latin native ‘quadri’ and also ‘latus’ an interpretation four and side respectively. Therefore, identify the properties of quadrilaterals is important when trying to identify them from other polygons.

You are watching: A parallelogram with four congruent sides and four right angles

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

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

This is what you’ll review in the article:

Here is a video explaining the properties of quadrilaterals:

The diagram given below shows a square ABCD and also the amount of its inner angles. All the interior angles sum up to 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 space equalAll sides space equal and, the contrary sides room parallel to every otherDiagonals bisect each various other perpendicularlySum of any type of two surrounding angles is 180°Rhombus formulas – Area and perimeter that a rhombus

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

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

These practice questions will assist you solidify the nature of rhombus

### Trapezium

A trapezium (called Trapezoid in the US) is a square that has actually 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.

Properties that Trapezium

A trapezium is a quadrilateral in i beg your pardon the following one property:

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

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

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

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

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

The below image likewise summarizes the nature of quadrilaterals:

The listed below table summarizes the recipe on the area and also perimeter the different varieties 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 exercise the application of properties of quadrilateral on the complying with sample questions:

### GMAT Quadrilaterials practice Question 1

Adam desires to develop a fence around his rectangular garden of size 10 meters and also width 15 meters. How plenty of meters of fence he need to buy to fence the entire garden?

20 meters25 meters30 meters40 meters50 metersSolution

Step 1: Given

Adam has a rectangle-shaped garden.It has a size of 10 meters and a broad of 15 meters.He desires to construct a fence approximately it.

Step 2: to find

The length forced to build the fence approximately the whole garden.

Step 3: Approach and also Working out

The fence can only it is in built about the external sides of the garden.

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

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

Therefore, alternative E is the exactly answer.

### GMAT Quadrilaterials practice Question 2

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

Step 2: come find

The full cost to repaint the wall.

Step 3: Approach and also Working out

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

Hence, the exactly answer is option E.

See more: How Many 4 Digit Combinations Are There, What Are All The Possible 4 Number Combinations

We expect by currently you would have learned the different types of quadrilaterals, their properties, and also formulas and how to use these ideas to solve questions on quadrilaterals. The application of quadrilaterals is essential to deal with geometry concerns on the GMAT. If you space planning to take it the GMAT, we can aid you with high-quality study product which girlfriend can access for totally free by registering here.

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