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Perimeter of a Square


A square is a regular quadrilateral and it has four equal sides and four equal angles (90 degree angle or right angles).

A square quadrilateral with vertices ABCD would be denoted by ABCD. The perimeter of a square (quadrilateral) is given by:


P = 4a
Where a is the length of each side.

Properties of square:
·  Diagonals of a square (quadrangle) bisect each other
·  Diagonals of a square (quadrangle) bisect its angles.
·  Diagonals of a square (quadrangle) are perpendicular.
·  Opposite sides of a square (quadrangle) are both parallel and equal.
·  All four angles of a square (quadrangle) are equal. (Square is 360/4 = 90 degrees, so every angle of a square (quadrangle) is a right angle.)
·  The diagonals of a square (quadrangle) are equal.


Example 1: Find the area and perimeter of the square whose side length is 4 meters.
Solution:
Given that:

a = 4m
Area of square = a2 = 4 × 4 = 16 m2
Perimeter of the square = 4 × 4 = 16 m


Example 2: Find the perimeter of square whose sides are 16 cm in length.
Solution:

Perimeter of the square:

P = 4a
P = 4 × 16 cm
P = 64 cm
Hence, the perimeter of square is 64 cm.

Example 3: What is the perimeter of a square, if the length of each side is 13 ft?
Solution:
The length of each side of a square is 13ft.
The perimeter of a square:
P = 4 × a
P = 4 × 13
P = 52 ft
The perimeter of the square is 52 ft.



Example 4: The perimeter of a square is 24 cm. What would the length of its sides be, if its perimeter is increased by 4 cm?
Solution:
New perimeter of the square = 24 + 4 = 28 cm.
New perimeter of the square = 4 × the new length of a side of the square
Let the new length of a side of the square = l cm

a = 7 cm


Example 5: The area of a square park is 225 m2. Find its perimeter.
Solution:
Given:
Since the area is 225 m
2, the length of the sides can easily be determined:
A = s²
225 = s²
s = 15m

Thus, the perimeter of park is:
P = 4 × s.
P = 4 x 15 m.
P = 60 m.


Example 6: Find the perimeter of the square, whose side length is 9.2 meters.
Solution:
Given: Side length (a) = 9.2 meters
Perimeter of the square
= 4 × a
  = 4 × 9.2
Perimeter of the square = 36.8 meters.

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