Parallelogram And Rectangle
Posted : admin On 1/26/2022Explain why it is not a rectangle. Look at each figure. Read each of the attributes. Place an X in the box if it appears to be an attribute of the figure pictured. What is true of all the figures? All of the figures above are parallelograms. Ring all the parallelograms below. Using what you know that is true of all parallelograms to help you. A parallelogram is a foursided shape in which the opposite sides are parallel. A rectangle (and a square) is a foursided shape in which the opposite sides are parallel and all corners are 90.
A rectangle is a foursided closed figure with each side making a right angle with another. A rectangle is also a parallelogram, the only difference lies in the angles constituting the figure. Like other parallelograms, opposite sides in a rectangle are parallel to each other. Its sides are generally called Lengths and Breadths. A rectangle is a parallelogram with four right angles with two concurring sides. A rhombus, which is occasionally called a diamond, is a parallelogram with four concurring sides. And a square is a parallelogram possessing four right angles and four concurring sides. But there’s some more! A rectangle is a square if and only if its diagonals are perpendicular. If the diagonals in a rectangle are perpendicular, then the rectangle is a square. What is a parallelogram that is not a rectangle? A parallelogram is a quadrilateral with 2 pairs of opposite, equal and parallel.

In Euclidean geometry, a quadrilateral is a foursided 2D figure whose sum of internal angles is 360°. The word quadrilateral is derived from two Latin words ‘quadri’ and ‘latus’ meaning four and side respectively. Therefore, identifying the properties of quadrilaterals is important when trying to distinguish them from other polygons.
So, what are the properties of quadrilaterals? There are two properties of quadrilaterals:
 A quadrilateral should be closed shape with 4 sides
 All the internal angles of a quadrilateral sum up to 360°
In this article, you will get an idea about the 5 types of quadrilaterals and get to know about the properties of quadrilaterals.
This is what you’ll read in the article:
 Rectangle
 Square
 Parallelogram
 Rhombus
 Trapezium
Here is a video explaining the properties of quadrilaterals:
The diagram given below shows a quadrilateral ABCD and the sum of its internal angles. All the internal angles sum up to 360°.
Thus, ∠A + ∠B + ∠C + ∠D = 360°
Different types of quadrilaterals
There are 5 types of quadrilaterals on the basis of their shape. These 5 quadrilaterals are:
 Rectangle
 Square
 Parallelogram
 Rhombus
 Trapezium
Let’s discuss each of these 5 quadrilaterals in detail:
Rectangle
A rectangle is a quadrilateral with four right angles. Thus, all the angles in a rectangle are equal (360°/4 = 90°). Moreover, the opposite sides of a rectangle are parallel and equal, and diagonals bisect each other.
Properties of rectangles
A rectangle has three properties:
 All the angles of a rectangle are 90°
 Opposite sides of a rectangle are equal and Parallel
 Diagonals of a rectangle bisect each other
Rectangle formula – Area and perimeter of a rectangle
If the length of the rectangle is L and breadth is B then,
 Area of a rectangle = Length × Breadth or L × B
 Perimeter of rectangle = 2 × (L + B)
Are you planning to enroll in a US business school? Let us help you conquer the first step of the process i.e., taking the GMAT. Take a free GMAT mock to understand your baseline score and start your GMAT prep with our free trial. We are the most reviewed online GMAT Prep company with 2060+ reviews on GMATClub.
Square
Square is a quadrilateral with four equal sides and angles. It’s also a regular quadrilateral as both its sides and angles are equal. Just like a rectangle, a square has four angles of 90° each. It can also be seen as a rectangle whose two adjacent sides are equal.
Properties of a square
For a quadrilateral to be a square, it has to have certain properties. Here are the three properties of squares:
 All the angles of a square are 90°
 All sides of a square are equal and parallel to each other
 Diagonals bisect each other perpendicularly
Square formula – Area and perimeter of a square
If the side of a square is ‘a’ then,
 Area of the square = a × a = a²
 Perimeter of the square = 2 × (a + a) = 4a
Scoring a Q5051 on the GMAT helps you get a 700+ GMAT score. Why don’t you start preparing for the GMAT with our free prep resources and start your journey of getting a Q5051 on the GMAT. Learn from Carrie Law who improved from Q35 to Q50 in 3 weeks.
Parallelogram
A parallelogram, as the name suggests, is a simple quadrilateral whose opposite sides are parallel. Thus, it has two pairs of parallel sides. Moreover, the opposite angles in a parallelogram are equal and its diagonals bisect each other.
Properties of parallelogram
A quadrilateral satisfying the belowmentioned properties will be classified as a parallelogram. A parallelogram has four properties:
 Opposite angles are equal
 Opposite sides are equal and parallel
 Diagonals bisect each other
 Sum of any two adjacent angles is 180°
Parallelogram formulas – Area and perimeter of a parallelogram
If the length of a parallelogram is ‘l’, breadth is ‘b’ and height is ‘h’ then:
 Perimeter of parallelogram= 2 × (l + b)
 Area of the parallelogram = l × h
Rhombus
A rhombus is a quadrilateral whose all four sides are equal in length and opposite sides are parallel to each other. However, the angles are not equal to 90°. A rhombus with right angles would become a square. Another name for rhombus is ‘diamond’ as it looks similar to the diamond suit in playing cards.
Properties of rhombus
A rhombus is a quadrilateral which has the following four properties:
 Opposite angles are equal
 All sides are equal and, opposite sides are parallel to each other
 Diagonals bisect each other perpendicularly
 Sum of any two adjacent angles is 180°
Rhombus formulas – Area and perimeter of a rhombus
If the side of a rhombus is a then, perimeter of a rhombus = 4a
If the length of two diagonals of the rhombus is d_{1} and d_{2} then the area of a rhombus = ½ × d_{1} × d_{2}
Trapezium
A trapezium (called Trapezoid in the US) is a quadrilateral which has only one pair of parallel sides. The parallel sides are referred to as ‘bases’ and the other two sides are called ‘legs’ or lateral sides.
Properties of Trapezium
A trapezium is a quadrilateral in which the following one property:
 Only one pair of opposite sides are parallel to each other
Trapezium formulas – Area and perimeter of a trapezium
If the height of a trapezium is ‘h’ (as shown in the above diagram) then:
 Perimeter of the trapezium= Sum of lengths of all the sides = AB + BC + CD + DA
 Area of the trapezium = ½ × (Sum of lengths of parallel sides) × h = ½ × (AB + CD) × h
Properties of quadrilaterals
The below table summarizes all the properties of the quadrilaterals that we have learned so far:
The below image also summarizes the properties of quadrilaterals:
Important quadrilateral formulas
The below table summarizes the formulas on area and perimeter of different types of quadrilaterals:
Further reading:
Quadrilateral questions
Let’s practice the application of properties of quadrilaterals on the following sample questions:
Question 1
Adam wants to build a fence around his rectangular garden of length 10 meters and width 15 meters. How many meters of the fence he should buy to fence the entire garden?
 20 meters
 25 meters
 30 meters
 40 meters
 50 meters
Solution
Step 1: Given
 Adam has a rectangular garden.
 It has a length of 10 meters and a width of 15 meters.
 He wants to build a fence around it.
Step 2: To find
 The length required to build the fence around the entire garden.
Step 3: Approach and Working out
The fence can only be built around the outside sides of the garden.
 So, the total length of the fence required= Sum 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 but the perimeter of the garden.
 Perimeter = 2 × (10 + 15) = 50 metres
Hence, the required length of the fence is 50 meters.
Therefore, option E is the correct answer.
Question: 2
Steve wants to paint one rectangularshaped wall of his room. The cost to paint the wall is $1.5 per square meter. If the wall is 25 meters long and 18 meters wide, then what is the total cost to paint the wall?
 $ 300
 $ 350
 $ 450
 $ 600
 $ 675
Solution
Step 1: Given
 Steve wants to paint one wall of his room.
 The wall is 25 meters long and 18 meters wide.
 Cost to paint the wall is $1.5 per square meter.
Step 2: To find
 The total cost to paint the wall.
Step 3: Approach and Working out
 A wall is painted across its entire area.
 So, if we find the total area of the wall in square meters and multiply it by the cost to paint 1 square meter of the wall then we can the total cost.
 Area of the wall = length × Breadth = 25 metres × 18 metres = 450 square metre
 Total cost to paint the wall = 450 × $1.5 = $675
Hence, the correct answer is option E.
We hope by now you would have learned the different types of quadrilaterals, their properties, and formulas and how to apply these concepts to solve questions on quadrilaterals. The application of quadrilaterals is important to solve geometry questions on the GMAT. If you are planning to take the GMAT, we can help you with highquality study material which you can access for free by registering here.
Here are a few more articles on Math:
If you are planning to take the GMAT, we can give you access to quality online content to prepare. We are the most reviewed GMAT prep company on gmatclub with more than 2060 reviews.
Why don’t you take a free trial and judge for yourself?
Write to us at [email protected] in case of any query.
FAQs
What are the different types of quadrilaterals?There are 5 types of quadrilaterals – Rectangle, Square, Parallelogram, Trapezium or Trapezoid, and Rhombus.
Where can I find a few practice questions on quadrilaterals?You can find a few practice questions on quadrilaterals in this article.
What is the sum of the interior angles of a quadrilateral?Parallelogram And Rectangle
The sum of interior angles of a quadrilateral is 360°.