Finding the perimeter of a square: formula and tasks

Contents

In this publication, we will consider how to calculate the perimeter of a square and analyze examples of solving problems.

Content

Perimeter Formula

Perimeter (P) of a square is equal to the sum of the lengths of its sides.

P = a + a + a + a

Since all sides of a square are equal, the formula can be expressed as a product:

P = 4 ⋅ a

The perimeter (P) of a square is equal to the product of the length of its diagonal and the number 2√2:

P = d ⋅ 2√2

This formula follows from the ratio of the lengths of the side (a) and diagonal (d) of the square:

d = a√2.

Task 1

Find the perimeter of a square if its side is 6 cm.

Decision:

We use the formula in which the value of the side is involved:

P = 6 cm + 6 cm + 6 cm + 6 cm = 4 ⋅ 6 cm = 24 cm.

Task 2

Find the perimeter of a square whose diagonal is √2 see

1 Solution:

Taking into account the value known to us, we use the second formula:

P = √2 cm ⋅ 2√2 = 4 cm.

2 Solution:

Express the length of the side in terms of the diagonal:

a = d / √2 = √2 cm/√2 = 1 cm.

Now, using the first formula, we get:

P = 4 ⋅ 1 cm = 4 cm.