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Parallelogram Questions and Answers

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Question 14 The Grammar School at Leeds 11 Pus Maths Entrance Paper 2021

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Question 07 - Christs Hospital 11 Plus Maths Entrance Examination 2023

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Coordinates, Parallelogram, Area and Scale drawings

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Coordinates, Parallelogram, Area and Perimeter and Triangle

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Scale drawing, Coordinates, Triangle and Parallelogram

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Properties of Parallelograms for 11 Plus Exams

1. What is a Parallelogram? 

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.

11+ Topicwise Parallelogram Article Image 01

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.             

1.1 Properties of parallelogram

Let us look at all the properties of a parallelogram.

11+ Topicwise Parallelogram Article Image 02

  • Opposite sides are equal. 

        Here, AB = CD and BC = AD

  • Opposite sides are parallel.

        Here, AB is parallel to CD and BC is parallel to AD.

  • Opposite angles are equal. 

        Here, a = c, b = d

  • Adjacent angles add up to 180 degrees. 

        Here, a + b = 180°, b + c = 180°, c + d = 180°, d + a = 180°

2. Working out angles in a parallelogram

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.

2.1 Solved example

ABCD is a parallelogram. If a = 65°, calculate the size of angle x.

11+ Topicwise Parallelogram Article Image 03

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.

3. Perimeter and Area of parallelogram

Perimeter of parallelogram: It is the sum of all the four sides of the parallelogram.

For the parallelogram shown below,

11+ Topicwise Parallelogram Article Image 04

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.

11+ Topicwise Parallelogram Article Image 05

Area of a parallelogram = b × h , where b is the base and h is the vertical height of the parallelogram.

3.1 Solved examples

Example 1:

What is the perimeter of the parallelogram shown below, if a = 15 cm, b = 12 cm?

11+ Topicwise Parallelogram Article Image 06

 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.

11+ Topicwise Parallelogram Article Image 07

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.

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