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Perimeter of a Square
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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
= a
^{2}
= 4 × 4 = 16 m
^{2}
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 m
^{2}
. 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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