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°In this article, you will get an idea around the 5 varieties of quadrilaterals and get come know about the properties of quadrilaterals.

This is what you’ll review in the article:

Different types of quadrilaterals

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

These exercise questions will help you solidify the properties of trapezium

## Properties of quadrilaterals

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:

## Important quadrilateralformulas

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 |

**Further reading:**

## Quadrilateral exercise Question

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**

**Step 2: to find**

**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 metresHence, 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**

**Step 2: come find**

**Step 3: Approach and also Working out**

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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