Last modified on November 18th, 2021

chapter outline

 

Area of Square

Area of a square is the number of unit squares needed to fill in a square. It is simply defined as the area or the space occupied by it. Since the area of a square is the product of its two sides, the measurement is done in square units such as m2, cm2, and mm2.

Formulas

Using Side Length

The basic formula to calculate the area of a square is given below:

Area of Square

Let us solve few examples to understand the concept better.

Find the area of a square chamber of side 20 m.

Solution:

As we know,
Area (A) = a2, here a = 20 m
 = (20 × 20) m2
= 400 m2

Find the area of a square-shaped swimming pool with side 33 feet.

Solution:

As we know,
Area (A) = a2, here a = 33 ft
= (33 × 33) ft2
= 1089 ft2

Using Diagonal

The formula to calculate the area of a square when only diagonal is known is given below:

Area of Square Using Diagonal

Derivation

Area of Square Using Diagonal Derivation

In square ABCD,

Applying Pythagoras theorem, we get

d2 = a2 + a2

=> d2 = 2a2

=> d = a × √2

=> a = d/√2

Squaring both sides, we get

=> a2 = d2/2

Since, a2 = area (A) of square, the above equation can be written as

Area (A) = d2/2

Let us solve an example to understand the concept better.

Find the area of a square with a diagonal of 16 cm.

Solution:

Here, we will use an alternative formula to calculate the area of a square
Area (A) = d2/2, here d = 16 cm
 = (16)2/2 cm2
 = 128 cm2

Using Perimeter

The formula to calculate the area of a square when only the perimeter is known is given below:

Area of Square Using Perimeter

Derivation

As we know,

Perimeter (P) = 4 × side = 4a

=> a = P/4

Now, as we know

Area (A) = a2

Area (A) = (P/4)2

Let us solve a few examples to understand the concept better.

Find the area of a square park with a perimeter of 200 cm.

Solution:

As we know,
Area (A) = (P/4)2, here P = 200
= (200/4)2 cm2
= (50 × 50) cm2
 = 2500 cm2
Alternative Method
As we know,
Perimeter (P) = 4 × side, here P = 200
=> 200 = 4 × side
=> side = 200/4 = 50 cm
Now, as we know
Area (A) = a2, here a = 50 cm
 = (50 × 50) cm2
 = 2500 cm2
Thus, the area of the square park of perimeter 200 cm is 2500 cm2

Find the cost of cementing a square floor of side 15 m if the rate of cementing is $10 per m².

Solution:

As we know,
Area (A) = a2, here a = 15 m
= (15 × 15) m2
= 225 m2
Now, since the rate of cementing is $10 per m²
Total cost of cementing the square floor = $ (225 × 10)
= $2250

Last modified on November 18th, 2021

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