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 of16 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 of200 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
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