AREA OF SQUARE
A square is a four-sided closed figure where the lengths of all the four sides will be equal and each vertex angle will be right angle or 90o as shown below.
Formula for Area of a Square
Let s be the length of each side of a square.
Then, the formula for area of a square :
Area = s2
Let d be the length of each diagonal of a square.
Then, the formula for area of a square :
Area = 1/2 ⋅ d2
Examples
Example 1:
Find the area of the square having side length 24 cm.
Solution:
When the length of a side is given, formula for area of a square :
= s2
Substitute 24 for s.
= 242
= 576
So, area of the square is 576 square cm.
Example 2:
If the area of a square is 64 square inches, then find the length of each side.
Solution:
Area of the square = 64 in2
S2 = 64
Find positive square root on both sides.
√s2 = √(8 ⋅ 8)
S = 8
So, the length of each side of the square is 8 inches.
Example 3:
The square has side length 250 cm. Find its area in square meter.
Solution:
When the length of a side is given, formula for area of a square :
= s2
Substitute 250 for s.
= 2502
= 62500 cm2 -----(1)
We know
100 cm = 1 m
Square both sides.
(100 cm)2 = (1 m)2
1002 cm2 = 12 m2
10000 cm2 = 1 m2
Therefore, to convert centimeter square into meter square, we have to divide by 10000.
(1)-----> Area of the square = 62500 cm2
Divide the right side by 10000 to convert cm2 into m2.
Area of the square = (62500 / 10000) m2
= 6.25 m2
So, the area of the square is 6.25 square meter.
Example 4:
If the length of each diagonal is 2√2 cm, then find its area.
Solution:
When the length of a diagonal is given, formula for area of a square :
= 1/2 ⋅ d2
Substitute 2√2 for d.
= 1/2 ⋅ (2√2)2
Simplify.
= 1/2 ⋅ (4 ⋅ 2)
= 1/2 ⋅ (8)
= 4
So, the area of the square is 4 square cm.
Example 5:
If the lengths of the diagonals of two squares are in the ratio 2 : 5. then find the ratio of their areas.
Solution:
From the ratio 2 : 5, let the diagonals of two squares be 2x and 5x respectively.
When the length of a diagonal is given, formula for area of a square :
= 1/2 ⋅ d2
|
Area of 1st square = 1/2 ⋅ (2x)2 = 1/2 ⋅ (4x2) = 4x2 / 2 |
Area of 2nd square = 1/2 ⋅ (5x)2 = 1/2 ⋅ (25x2) = 25x2 / 2 |
Ratio of the areas :
= (4x2 / 2) : (25x2 / 2)
Multiply each term of the ratio by 2.
= 4x2 : 25x2
Divide each term by x2.
= 4 : 25
So, the ratio of the areas of two squares is 4 : 25.
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