draw a squre whose each side measure 5.9cm .find its area and perimeter
Answers
The formula of perimeter and area of square are explained step-by-step with solved examples.
If 'a' denotes the side of the square, then, length of each side of a square is 'a' units
perimeter and area of square
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 = a² square units
Therefore, a² = A Here, a is the side of the square.
Therefore, a² = √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 = √(a² + a²) = √(2a²^2) = a√2 units
Worked-out 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 cm²
= 121 cm²
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 m² = 169 m².
3. The area of a square is 144 m². Find its perimeter.
Solution:
Area of square = side × side
Given; area of square = 144 m²
Therefore, side² = 144 m²
Therefore, side = √(144 m²) = √(2 × 2 × 2 × 2 × 3 × 3) m² = 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 m².
Solution:
Perimeter of square courtyard = 144 m
Therefore, side of the square courtyard = 144/4 = 36 m
Therefore, area of square courtyard = 36 × 36 m² = 1296 m²
For 1 m², the cost of cementing = $5
For 1296 m², 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