The Perimeter and Area of the Square are used to measure the length of the boundary and space occupied by the square. These are two important formulas used in **Mensuration**. Perimeter and Area of the Square formulas are used in the 2-D geometry.

Square is a regular quadrilateral where are the sides and angles are equal. The concepts of the Perimeter and Area Square formula, Derivation, Properties, are explained here. The solved examples with clear cut explanations are provided in this article. Students can understand how and where to use the formulas of Area and Perimeter of Square.

### What is the Area and Perimeter of the Square?

**Area of a square:** The area of the square is defined as the region covered by the two-dimensional shape. The units of the area of the square are measured in square units i.e., sq. cm or sq. m.

**Perimeter of a square:** The perimeter of the square is a measure of the length of the boundaries of the square. The units of the perimeter are measured in cm or m.

### Area of Square Formula

The area of the square is equal to the product of the side and side.

Area = Side × Side sq. units

A = s² sq. units

### Perimeter of Square Formula

The perimeter of the square is the sum of the lengths.

P = s + s + s +s

P = 4s units

Where s is the side of the square.

### Diagonal of Square Formula

The square has two diagonals with equal lengths. The diagonal of the square is greater than the sides of the square.

- The relationship between d and s is d = a√2
- The relationship between d and Area is d = √2A

### What is Square?

A square is a regular polygon in which all four sides are equal. The measurement of the angles of the square is also equal.

### Properties of Squares

The properties of the square are similar to the properties of the rectangle. Go through the properties of squares from the below section.

- All sides of the squares are equal.
- It has 4 sides and 4 vertices.
- The interior angles of the square are equal to 90º
- The diagonlas of square bisect at 90º
- The diagonals of the square are divided into two isosceles triangles.
- The opposite sides of the squares are parallel to each other.
- Each half of the square is equal to two rectangles.

### Solved Problems on Perimeter and Area of Square

Below we have provided the solved examples of perimeter and area of a square with a brief explanation. Scroll down this page to check out the formulas of Area and Perimeter of Square.

**1. What is the Area and Perimeter of the square if one of its sides is 4 meters?**

Solution:

Given the side of the square is 4 meters.

Area of the square = s × s

A = 4 m × 4 m

A = 16 sq. meters

The perimeter of the square = 4s

P = 4 × 4 m

P = 16 meters.

Therefore the area and perimeter of the square are 16 sq. meters and 16 meters.

**2. Find the area of the square if the side is 10 cm?**

Solution:

Given,

s = 10 cm

Area of the square = s × s

A = 10 cm × 10 cm

A = 100 sq. cm

Therefore the area of the square is 100 sq. cm

**3. The perimeter of the square is 64 cm. Find the area of the square?**

Solution:

Given,

The perimeter of the square is 64 cm

P = 4s

64 cm = 4s

s = 64/4 = 16 cm

Thus the side of the square is 16 cm.

Now the find the area of the square.

Area of the square = s × s

A = 16 cm × 16 cm

A = 256 sq. cm

Therefore the area of the square is 256 sq. cm.

**4. If the area of the square is 81 cm², then what is the length of the square?**

Solution:

Given,

A = 81 cm²

Area of the square = s × s

81 sq. cm = s²

s² = 81 sq. cm

s = √81 sq. cm

s = 9 cm

Thus the length of the square is 9 cm.

**5. The length of the square is 25 cm. What is the area of the square?**

Solution:

Given,

The length of the square is 25 cm

Area of the square = s × s

A = 25 × 25

A = 625 sq. cm

Therefore the area of the square is 625 sq. cm.

### FAQs on Perimeter and Area of Square

**1. How to find the perimeter of the square?**

Add all the sides of the square to find the perimeter of the square.

**2. What is the formula for the perimeter of a square?**

The Perimeter of Square formula is sum of the lengths i.e, side + side + side + side = 4s

**3. What is the formula for the area of the square?**

The area of the square formula is the product of side and side. A = s × s.