Perimeter of square :
Here we are going to see some example problems to understand this topic. A shape which is having four equal sides is called a square.Now let us see the formula to find perimeter of square.
Perimeter of a square = a + a + a + a
Example 1 :
Find the perimeter of the square having side length 24 cm
Perimeter of a square = 4a
here a = 24 cm
= 4 ( 24 )
= 96 cm
Hence, perimeter of the square is 96 cm
Example 2 :
Find the perimeter of the square having side length 15 cm
Perimeter of a square = 4a
here a = 15 cm
= 4 ( 15 )
= 60 cm
Therefore perimeter of the square is 60 cm
Example 3 :
A square is of area 64 cm². What is its perimeter?
Area of a square = 64 cm²
a² = 64 cm²
a = √ 64
a = √8 x 8
a = 8 cm
Now we have to find the perimeter
Perimeter of the square = 4a
= 4 (8)
= 32 cm
Therefore perimeter of the square is 32 cm
Example 4 :
Perimeter of a square is 20 cm. What is its area?
Perimeter of a square = 20 cm
4a = 20 ==> a = 5 cm
Area of a square = a² = 5² ==> 25 cm²
Therefore area of the square is 25 cm²
Example 5 :
Find the perimeter of the square whose diagonal is measuring 4cm.
In the above square we have two right triangles. Those are ⊿ ACB and ⊿ ADC. In ⊿ ACB right angled at B. The side which is opposite to this angle is called hypotenuse side. We can find the other sides using Pythagorean theorem.
AC² = AB² + BC²
Since all sides are equal in square the sides AB and BC are equal in length.
Let AB = x so BC = x
AC² = x² + x² ==> 4² = 2x² ==> x² = 16/2 ==> x² = 8
x = √8
x = √2 x 2 x 2
x = 2 √2 cm
Hence, length of all sides = 2 √2 cm
Perimeter of square = 4a
= 4 (2 √2)
= 8 √2 cm
Example 6 :
The perimeter of two squares are 40 cm and 32 cm. Find the perimeter of third square whose area is equal to the difference of the area of two squares.
Let "a" and "b" are side length of first and second squares respectively.
Perimeter of first square = 40 cm
4 a = 40 ==> a = 10
Perimeter of second square = 32 cm
4 b = 32 ==> b = 8
Area of third square = 10 ² - 8² ==> 36 cm²
Side length of third square = √36 ==> 6 cm
Perimeter of third square = 4 (6) = 24 cm
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