Parallelogram - It is a quadrilateral with opposite sides equal and parallel. Diagonally opposite angles in a parallelogram are also equal. Since a parallelogram is also a quadrilateral, the sum of all the angles of a quadrilateral is 360 degrees.
Quadrilaterals like squares and rectangles also have opposite sides equal and parallel. Diagonally opposite angles are also equal in these shapes(squares and rectangles have all right angles). So Square and rectangle is also a parallelogram.
Rhombus is also a parallelogram as it has opposite sides equal and parallel and opposite angles are also equal.
Other quadrilaterals like trapezium and kite do not satisfy the properties of a parallelogram.
Let us look at all the properties of a parallelogram.
Here, AB = CD and BC = AD
Here, AB is parallel to CD and BC is parallel to AD.
Here, a = c, b = d
Here, a + b = 180°, b + c = 180°, c + d = 180°, d + a = 180°
We have seen that angles in a parallelogram add up to 360 degrees. Using this and the above mentioned properties on parallelogram, let us try to work out some of the missing angles in quadrilaterals.
ABCD is a parallelogram. If a = 65°, calculate the size of angle x.
Solution: x and a are adjacent angles.
From the property of parallelogram, adjacent angles add up to 180°.
So x + a = 180°
x + 65° = 180°
x = 180° - 65° = 115°
The value of x is 115°.
For the above example question, you can also try to work out the remaining angles of the parallelogram using the properties of a parallelogram.
Perimeter of parallelogram: It is the sum of all the four sides of the parallelogram.
For the parallelogram shown below,
Perimeter = a + b + a + b
= 2a + 2b = 2(a+b)
Formula for the perimeter of a parallelogram is similar to the perimeter of a rectangle.
Area of a parallelogram:
Below is the formula to find the area of the parallelogram using its height and base.
Area of a parallelogram = b × h , where b is the base and h is the vertical height of the parallelogram.
Example 1:
What is the perimeter of the parallelogram shown below, if a = 15 cm, b = 12 cm?
Solution: Perimeter of a parallelogram = 2(a+b)
= 2(15+12)
= 54 cm
Example 2:
The diagram below shows a parallelogram drawn inside a square.
What is the area of the shaded region?
Solution: Area of the shaded region is nothing but the area of the parallelogram.
Base of the parallelogram b = 12 - 2.5 = 9.5 feet
Height of the parallelogram h= Side of the square = 12 feet
Area of a parallelogram = b × h
= 9.5 × 12 = 114 feet²
Area of the shaded region is 114 feet².
What counts as a "good" score will vary depending on the school you want to attend. The standardized 11 Plus test score average across the country is roughly 100. The highest average in some areas is 111. The lowest scores would often fall between 60 and 70, while the highest scores would normally fall between 130 and 140. To achieve excellent marks on 11+ Maths Exams, practice 11+ Maths topic-wise questions.
The best way to prepare for the 11+ Maths Exam is by practicing 11+ Maths topic-wise questions regularly.
Maths online subscriptions are “Non-Refundable“. No refunds can be issued for any reason. This is because of the nature of digital products.
You should, therefore, make sure that the Maths online subscriptions fulfil your needs before you subscribe.
As these are digital products, we advise parents to go through our Free Past Papers provided on our website and once decided they can buy subscriptions.
The majority of the 11 Plus Maths questions are mathematical problem-solving, where pupils need to understand and apply mathematical concepts. With regular practice of 11+ Maths Topic-wise questions, you will pass the 11-plus Maths Exam with a high score.
The children must master the following topics for the 11 plus exams
Get 10,000+ Topic-wise questions by subscribing to our 11+ Maths Topic-wise questions. These questions are collected from 180+ Maths past papers.
11 Plus Maths Past Papers Subscription
Any PiAcademy Memberships are for 1 year (366 days), We give Instant unlock to all exam Resources So that you can plan your 11+ Preparation according to your convenience and as per our Planner Spreadsheets.
Hurry! 11+ Exams are approaching in 6 months. High competition. Most parents fail to do structured planning for the 11+ Exam preparation.
Get a plan and strategy from 11+ Expert Tutors. Avoid the common mistakes that other parents make.
© 2014 - 2025 PiAcademy Limited, All Rights Reserved