Perimeter of a Square
A square is a type of rectangle in which the adjacent sides are equal. In other words, all the sides of a square are equal.
Following are the properties of a square:
(i) All the angles in a square are the same and equal 90º.
(ii) All the sides of a square are equal.
Perimeter of a square
The perimeter of a square is the total length of all the sides of the square. Hence we can find the perimeter of a square by adding all its four sides.
The perimeter of the given square is a + a + a + a. Since all sides of a square are equal, we only need one side to find its perimeter.
The perimeter of the given square is:
a + a + a + a = 4 a units.
Hence, the formula of the perimeter of a square = 4 × (length of any one side).
Tricky math problems with the squares:
Type I: Finding side length when only the perimeter is given.
Example 1. If the perimeter of the given square is 12 cm. What will be the length of its side?
Solution: Given, the perimeter of the square is 12 cm.
Let the side length be ‘a’ cm.
We know that, the perimeter of a square = 4 × (side length)
12=4×(a)
a = 3 cm
Type II: Finding sides using square properties.
Example 2.If a = 4 cm in the given square. Find b, c. and d.
Solution: Given that side a = 4 cm.
To find side b, c, and d we use the property of the square which states that all the sides of a square are equal.
Therefore, a = b = c = d = 4 cm
Type III: Finding perimeter when one of the sides is given.
Example 3. One of the sides of a square is 5 cm. What will be its perimeter?
Solution: Given, one side of the square is 5 cm.
We know that, the perimeter of a square = 4 × (side length)
= 4×(5)
= 20 cm
Example 4. The length of a side of the square wooden frame is 5 cm. Find the total length of the wood used in the frame.
Solution: Given, the length of a side of this wooden frame is 5 cm.
As we know, the perimeter of a square = 4× (side length)
= 4 (5)
= 20 cm
Hence, the total length of the wood used is 20 cm.
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