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.
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…
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.
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
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.
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