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Question 14 - Oundle School Second Form Mathematics 2021

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Question 21 Haberdashers Monmouth Girls School HABS Entrance Examination 2015

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Question 28 - Merchant Taylors School 11 Plus Maths Specimen Paper 2

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Question 19 - Merchant Taylors School 11 Plus Maths Specimen Paper 2

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Question 35-Merchant Taylors School 11 Plus Maths Entrance Examination 2021

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Mastering Rectangles for 11 Plus Exam

1. What is a Rectangle?

Rectangle shapes area all around us. It is one of the simplest 2D shapes with four sides. Opposite sides of the rectangle are equal and parallel.
All the internal angles in a rectangle are right angles, which means that each
angle in a rectangle measures 90°. It is a simple quadrilateral with two dimensions
length and width.

01 Rectangles

For the rectangle ABCD shown above,
It has four right angles.
Opposite sides are equal, so AB = CD, AD = BC.
AB is parallel to CD and AD is parallel to BC.

Diagonals: A rectangle has two diagonals that are equal in length and intersect in the centre.

02 Rectangles

For the above rectangle ABCD, AC and BD are the diagonals with AC = BD.

2. Working out Perimeter and Area of a Rectangle

Perimeter is the sum of all the sides of a rectangle. Let us look at the figure shown below to understand how to work out the perimeter of a rectangle,

03 Rectangles

Here, 

l is the length of the rectangle, and w is its width.

Perimeter of rectangle = Sum of all the sides of rectangle

                                      =l + w + l + w

                                      =2l + 2w

                                      =2(l + w)

Area of a rectangle is equal to its product of length and width. Area is always measured in square units.

            Area of rectangle = Length × Width

                                      = l × w

We can use the above formulas to find the perimeter and area of any rectangle using its length and width. Let us use this formula and try to solve some example questions.

2.1 Example Question on Perimeter of Rectangle

The plan shown below is of a garden. There is a 2 m wide path around
The edge of the garden, with a swimming pool inside the path.

04 Rectagnles

Work out the perimeter of :
a) Garden
b) Pool

Solution :

a) Garden is the outer rectangular shape shown in the plan

Length of the rectangular garden l =15 m 

Width of the rectangular garden w =12 m

Perimeter of rectangle =2(l+ w)

Perimeter of rectangular garden =2(15+12)

                                               =227

                                               =54 m

b) Pool is the inner rectangular shape shown in the plan

    Pool is 2 m wider from the garden.

    Length of the rectangular pool l =15 -(2+2)=11 m 

    Width of the rectangular pool w =12-(2+2)=8 m

     Perimeter of rectangle =2(l + w)

     Perimeter of rectangular pool =2(11+8)

                                                =219

                                                =38  m

2.2 Example Question on Area of Rectangle

Work out the area of the shaded rectangle in the figure shown below

05 Rectangles

Solution :

Length of the shaded rectangle l =12 cm - 4 cm = 8 cm

Width of the shaded rectangle w = 7 cm

Area of a rectangle = l × w

Area of the shaded rectangle = 87 = 56 cm²

Quiz Questions
35. Rectangle
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35. Rectangle Worksheet

 

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