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The total length of all four sides of the square is called the perimeter of a square. We will learn how to calculate the perimeter of a square, its formula and some solved examples for better understanding....Read MoreRead Less

A square is a special case of a quadrilateral all of whose sides are equal, and each angle is 90°.

We now know that the perimeter is the length of the boundary of any geometric shape. We discussed earlier that the square is made up of 4 equal sides, so the sum of all the four equal sides gives us its perimeter.

**The formula for perimeter of a square is: **

**P = 4 \(\times\) ****s**

Where s is the length of one of the sides of the square.

The side and perimeter can be expressed in the following units:

millimeter(mm), centimeter(cm), meter(m), kilometer(km), inch(in), feet(ft), yard(yd), mile(mi) and so on.

**Example 1:** Find the perimeter of a square whose side length is 4 inch.

**Solution:**

P = 4 \(\times\) s Write the formula for perimeter of square

P = 4 \(\times\) 4 Substitute 4 for s

P = 16

So, the perimeter of a square is 16 inches.

**Example 2:** Find the perimeter of a square desk whose edge length is 3 feet.

**Solution:**

P = 4 \(\times\) s Write the formula for perimeter of square

P = 4 \(\times\) 3 Substitute 3 for s

P = 12

So, the perimeter of a square desk is 12 feet.

**Example 3: **The perimeter of a square shaped garden is 40 yards. Find the side length of the garden.

**Solution:**

P = 4 \(\times\) s Write the formula for perimeter of square

40 = 4 \(\times\) s Substitute 40 for P

\(\frac{40}{4}\) = \(\frac{4\times s}{4}\) Divide each side by 4

10 = s

So, the side length of the garden is 10 yards.

**Example 4: **Jacob walks a total of 3200 meters on a square shaped path around the park. If he covered the entire path while covering this distance, then what is the length of one of the sides of the path.

**Solution:**

Jacob, walking along the edges of the square shaped park, completes one round, which is the perimeter of the park.

As the park is square shaped,

The perimeter of the park(P) = 4 length of one side of path(s)

3200 = 4 \(\times\) s Substitute 3200 for P

\(\frac{3200}{4}\) = \(\frac{4\times s}{4}\) Divide each by 4

800 = s

So, the length of one side of the path is 800 meters.

**Example 5:** James has a square plot with sides that are 50 feet in length. What is the boundary length of the plot? If fencing material costs $10 per foot, then find the costing of fencing the plot.

**Solution : **

Boundary length is equal to perimeter:

P = 4 \(\times\) s Write the formula for perimeter of square

P = 4450 Substitute 50 for s

P = 200

So, the length of his boundary is 200 feet.

Now to find the cost of fencing we need to multiply the perimeter found by the rate of fencing.

= 200 \(\times\) 10

= $2000

Therefore the cost of fencing the square plot that James has is $2000.

Frequently Asked Questions

There are three types of parallelograms:

- Rectangle
- Rhombus
- Square

A square has four angles, each angle measuring 90°, but on the other hand, a rhombus does not.

Yes, all the properties of a rectangle are found in squares.

- Both are parallelograms.
- Both have sides that are equal in length.
- Diagonals are perpendicular bisectors in both of these geometric shapes.

Area of square = \(s^2\), where s is the length of the side of the square.

Perimeter is a measure of distance, so all the units of distance are used as units to express perimeter. Such as millimeter(mm), centimeter(cm), meter(m), kilometer(km), inch(in), feet(ft), yard(yd), mile(mi) and so on.