Perimeter and Area of Square
The formula of perimeter and area of square are explained stepbystep with solved examples.
If 'a' denotes the side of the square, then, length of each side of a square is 'a' units
Perimeter of square = AB + BC + CD + DA = (a + a + a + a) units = 4a units
● Perimeter of the square = 4a units
We know that the area of the square is given by Area = side × side A = a × a sq. units Therefore, A = a^{2} square units Therefore, a^{2} = A Here, a is the side of the square. Therefore, a^{2} = √A Therefore, side of the square = √Area
● Side of the square = P/4 units ● Area of the square = a × a = (P/4)^{2} sq. units ● Area of square = 1/2 × (diagonal)^{2} sq. units ● Length of the diagonal = √(a^{2} + a^{2}) = √(2a^{2}^2) = a√2 units
Workedout examples on Perimeter and Area of the Square:
1. Find the perimeter and area of a square of side 11 cm.
Solution:
We know that the perimeter of square = 4 × side Side= 11 cm Therefore, perimeter = 4 × 11 cm = 44 cm Now, area of the square = (side × side) sq. units = 11 × 11 cm^{2} = 121 cm^{2}
2. The perimeter of a square is 52 m. Find the area of the square.
Solution:
Perimeter of square = 52 m But perimeter of square = 4 × side Therefore, 4 × side = 52 m Therefore, side= 52/4 m = 13m Now, the area of the square = (side × side) Therefore, area of the square = 13 × 13 m^{2} = 169 m^{2}
3. The area of a square is 144 m^{2}. Find its perimeter.
Solution:
Area of square = side × side Given; area of square = 144 m^{2} Therefore, side^{2} = 144 m^{2} Therefore, side = √(144 m^{2}) = √(2 × 2 × 2 × 2 × 3 × 3) m^{2} = 2 × 2 × 3 m = 12 m Now, the perimeter of the square = 4 x side = 4 × 12 m = 48 m
4. The length of the diagonal of a square is 12 cm. Find its area and perimeter.
Solution:
Diagonal of a square = 12 cm Area of square = 1/2 (d)^{2} = 1/2 (12)^{2} = 1/2 × 12 × 12 = 72 Side of a square = √Area = √72 = √(2 × 2 × 2 × 3 × 3) =2 × 3√2 = 6 × 1.41 = 8.46 cm Perimeter of square = 4 × 8.46 = 33.84 cm
5. The perimeter of a square courtyard is 144 m. Find the cost of cementing it at the rate of $5 per m^{2}.
Solution:
Perimeter of square courtyard = 144 m Therefore, side of the square courtyard = 144/4 = 36 m Therefore, area of square courtyard = 36 × 36 m^{2} = 1296 m^{2} For 1 m^{2}, the cost of cementing = $5 For 1296 m^{2}, the cost of cementing = $1296 × 5 = $6480
The above solved examples are explained how to solve perimeter and area of square with the detailed explanation.
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