11+ Maths Solved Topic Wise Questions

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.

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.

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,

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.

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

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