11+ Maths Solved Topic Wise Questions

1. What is a Square?

A square is a simple 2D shape with four equal sides and four equal right angles. Opposite sides of the square are parallel to each other. Thus a square has two pairs of parallel sides.

For the square ABCD shown above,

It has four right angles which can be seen from the figure.

All sides are equal, so AB = BC = CD = AD

Opposite sides are parallel, AB is parallel to CD and AD is parallel to BC.

2. Working out the perimeter and Area of a Square

Perimeter of a square is the sum of all sides of the square. Since a square has all equal sides, its perimeter will be four times the sides of the square. Let us try to understand this with the figure below.

a is the side of the square shown above.

Perimeter of square = Sum of all the sides of square

= a + a + a + a

= 4 × a

This is the simple formula to find the perimeter of the square using its side length.

Since a square has all sides of equal measure, the area will be length × width, which for the square will be side × side sq units.

So for the above square, where a is the side,

Area of square = side × side

= a × a

= a² sq. units

Area of any shape is always measured in square units, for example cm², m², in², etc…

2.1 Example Question on Perimeter of square

A wire that is l metres long is bent to form a square of side 65 cm.

Work out the value of l.

Solution: Since the wire is l metres long, l should be sum of all four sides, i.e, Perimeter of the square.

So l = Perimeter of the square

Side of the square (a) = 65 cm

Perimeter of the square = 4 × a

= 4 × 65

= 260 cm

Value of l is in metres, so we need to convert from cm to m.

Relation between metres and centimetres is 1 m = 100 cm

So 260 cm = 260 ÷ 100 = 2.6 m

The length of the wire l is 2.6 m.

2.2 Example Question on Area of a square

The diagram below is a scale drawing of a T shaped path made from identical squares of side 2 cm each.

What is the area of this path?

Solution: You can see there are five identical squares in the T shaped path.

Length of one side of the square (a) = 2 cm

Area of square = a²

Area of one square = 2 × 2 = 4 cm²

Total area of path = 5 × (Area of one square)

= 5 × 4

= 20 cm²