Perimeter of a Square

# Perimeter of a Square

## Perimeter of a Square

We know that the square is a plane figure or two-dimensional figure. All the sides of a square are equal and all the angles of a square measure 90°.

The perimeter of a closed two-dimensional figure is the length of its boundary. The units of measurement of perimeter are the same as that of length, i.e. cm, m or km.

To find the perimeter of a square, we add the measures of all its sides.

Let we have to find the perimeter of a given square ABCD.

Perimeter of the square ABCD = AB + BC + CD + DA

= AB + AB + AB + AB           (Since, AB = BC = CD = DA)

= 4 AB

= 4 × side

Thus, the perimeter of a square = 4 × side

If the length of each side of the square is s, then

Perimeter of a square = 4 × s

## Perimeter of a Square Formula

Perimeter of a square = 4 × s

Where s is the length of each side of the square.

## Perimeter of a Square Example

Example 1: Find the perimeter of a square, whose each side measures 6.5 cm.

Solution: Given: side of the square, s = 6.5 cm

Perimeter of a square = 4 × s

= 4 × 6.5 cm

= 26 cm

Example 2: A square plot is 75 m long. Find the length of the wire required to fence

all around it 4 times.

Solution: Given: length of the square plot, s = 75 m

Length of the wire to fence it one time = Perimeter of the square plot

= 4 × s

= 4 × 75 m

= 300 m

Length of the wire required to fence the square plot 4 times = 4 × 300 m = 1200 m

Hence, the total length of the wire required to fence the square plot is 1200 m.

Example 3: Aman takes 20 rounds of a square park which is 60 m long. Find the total distance covered by him in kilometres.

Solution: Given: length of the park, s = 60 m

Distance covered by Aman in 1 round = Perimeter of the park

= 4 × s

= 4 × 60 m

= 240 m

Total distance covered by Aman in 20 rounds = 20 × 240 m = 4800 m

Thus, the total distance covered in kilometres = 4800/1000 km

(Since 1 km = 1000 m)

= 4.8 km

Example 4: If the perimeter of a square field is 340 m, find the measure of each side of the square field.

Solution: Given: perimeter of the square field = 340 m

We know that,

Perimeter of a square = 4 × s

340 m = 4 × s

s = 340/4 = 85 m

Hence, the measure of each side of the square field is 85 m.

Example 5: Each side of a square photo frame measures 46 cm. If its border is 3 cm

wide, then find the perimeter of the picture.

Solution: Given: Side of the photo frame = 46 cm

Each side of the picture = 46 cm – (3 cm + 3 cm) = 40 cm

Thus, the perimeter of the picture = 4 × s

= 4 × 40

= 160 cm

Hence, the perimeter of the picture is 160 cm.

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