Session 5: Area of Square – Formula, Definition, Interactives and Examples

What is Area?

The area is the amount of surface enclosed by a closed two-dimensional figure. It is measured by the number of unit squares it takes to cover a two-dimensional shape. For example, if you count the small squares, you will find there are 15 of them. Therefore, the area is 3⋅5 or 15 unit².

---

Area of Square

A square is a plane figure whose all four sides are of equal lengths. The area of a square is the number of unit squares it takes to cover a square. Since all the sides of a square are equal, its area is the product of its two sides.

---

Formula for Area of Square

We know that a square is a rectangle whose base and height are equal.

[Figure 2]

Area_square=side×side

---

Area of Square – Examples

Example 1

Find the area of square whose side is 15 units.

We know,

Area of square = side × side

  =15×15
=225 units²

Example 2

Find the side length of a square of area 324 cm².

We know,

Area of square = side × side

∴ side of the square=\(\sqrt{Area of square}\)                                  

Example 3

The floor of a big room is in the shape of a rectangle of length 4 m and breadth 2.5 m. The floor is to be covered by square tiles each of side 20 cm. Find the number of tiles required.

The length of the rectangular room = 4 m = 400 cm.

The breadth of the rectangular room = 2.5 cm = 250 cm.

∴ Area of the rectangular room = length ×breadth

                                                       =(400×250) cm²

The side length of each square tile = 20 cm.

∴ Area of the square tile = side × side

                                            =(20×20) cm²

∴ Number of tiles required=\(\frac{Area of the floor of the room}{Area of each tile}\)                                             

Example 4

Allen bought a new house and planned to replace the carpet in two bedrooms. One bedroom is in the shape of a square, and the other is rectangular. The square bedroom has side lengths of 6 m, and the rectangular bedroom has a length of 11 m and a width of 5 m. Find out how much carpet is needed to cover both bedroom floors. Also, find the cost of the carpeting at the rate of ₹75 /m².

For Allen to figure out how much carpet he needs to buy for these two bedrooms, he needs to find the sum of each bedroom area.

His square bedroom has side lengths of 6 m.

∴  Area of the square bedroom = side × side

                                                       =6×6=36 m²

The other room is a rectangle with dimensions of 11 m by 5 m.

∴ Area of the rectangular bedroom = length × width

                                                              =11×5=55 m²

Allen wants to know the total area of his bedroom to know how much carpet to buy, so add the two areas together.

Total area =36+55=91 m²

Rate of carpeting = ₹75 /m²

∴ Total cost of carpeting = Total area × Rate of carpeting

=91×75
=₹6825

Example 5

The perimeter of a rectangle is equal to the perimeter of a square. If the side of the square is 6 feet and the length of the rectangle is 9 feet, then find the ratio of the area of the square and the rectangle.

The side of the square = 6 feet

The length of the rectangle = 9 feet

Let the width of the rectangle be w feet.

Since the perimeter of the rectangle is equal to the perimeter of the square,

Then,

Area_square:Area_rectangle=6×6:9×3
=36:27
=4:3

Example 6

From a square sheet of paper of side 14 cm, a strip of width 3 cm is removed along the border. Find the area of the removed strip of paper.

Side of the outer square sheet = 14 cm.

Width of the strip = 3 cm.

Side of the inner square sheet =14−2(3)=14−6=8 cm

Area of the outer square =14×14=196 cm²

Area of the inner square =8×8=64 cm²

Area of the removed strip = Area of the outer square − Area of the inner square

=196−64
=132 cm²

Remember this!

• The area is the amount of surface enclosed by a closed two-dimensional figure.
• The formula for the area of a square is: 
  Area_square=side×side