What is the area of a square?
The area of a square is defined as the total number of unit squares in the shape of a square.
In other words, it is defined as the space occupied by the square.
The formula for area of a square,
Area of a Square = a^{2}
(where a is the side of a square)
Area of a square using diagonals = 1/2 × d^{2}
What is the Perimeter of a Square?
The perimeter of a square is the distance covered by its four sides.
Perimeter surrounds or outlines the shape in a two-dimensional plane.
The formula for perimeter of a square,
Perimeter of a square = 4 side
Perimeter of a square using diagonals = 2√2 × d
Example 1 :
Find the perimeter of a square whose area is 120 m^{2}.
Solution :
Given, Area = 120 m^{2}.
Area of a Square = a^{2}
120 = a^{2}
a = √120
a = 10.95
Perimeter of a square = 4a
= 4(10.95)
Perimeter = 43.82 m
Example 2 :
Find the area of the square field whose perimeter is 240 m.
Solution :
Perimeter = 240 m.
Perimeter of a square = 4a
240 = 4a
240/4 = a
a = 60
Area of a Square = a^{2}
Area = 60^{2}
Area of the square field = 3600 m^{2}.
Example 3 :
A rope of length of 104 m is used to fence a square garden. What is the length of the side of the garden ?
Solution :
The length of rope is 104 m.
The perimeter of square fence is given as 104 m.
Perimeter of a square = 4a
104 = 4a
104/4 = a
a = 26 m
So the length of the side of the garden is 26 m.
Example 4 :
Lila has 16 square stamps of side 4 cm each. She glues them onto an envelope to form a bigger square. What area of the envelope does the bigger square cover?
Solution :
16 square shaped stamps can be arranged as 4 in each row.
So it forms 4 rows and 4 columns.
Side of the formed square s = 4 + 4 + 4 + 4
s = 16 cm
Area of a square = s^{2}
Area = 16^{2}
= 256 cm^{2}
So, the area of the bigger square is 256 cm^{2}.
Example 5 :
If the diagonal length of a square is 7 cm, find the square area, perimeter ?
Solution :
Area of a square using diagonals = 1/2 × d^{2}
= 1/2 × 7^{2}
= 1/2 × 49
Area = 24.5 cm^{2}
Perimeter of a square using diagonals = 2√2 × d
= 2√2 × 7
Perimeter = 19.8 cm
Example 6 :
The diagonals of two squares are in the ratio 2 : 5. Find the ratio of their areas.
Solution :
Let the diagonal of 1^{st }square be 2x.
The diagonal of a square formula = a√2
a√2 = 2x
a = 2x/√2
a = 2x/√2 × √2/√2
= (2x√2)/(√2)^{2}
= (2x√2)/2
a = √2x
Area of a square = a^{2}
= (√2x)^{2}
Area = 2x^{2}
Let the diagonal of 2^{nd}^{ }square be 5x.
The diagonal of a square formula = a√2
a√2 = 5x
a = 5x/√2
a = 5x/√2 × √2/√2
= (5x√2)/(√2)^{2}
a = (5x√2)/2
Area of a square = a^{2}
= [(5x√2)/2]^{2}
Area = (25x^{2})/2
Ratio of areas = 2x^{2} : (25x^{2})/2
Multiplying 2 on both areas, we get
= 4 : 25
So, the ratio of their areas is 4 : 25.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM