Area of square :
Here we are gong to see how to find area of the given square.
There are 3 ways to area of a square. We have to use one of the ways according to the information given in the question.
Area of the square = a²
Here "a" stands for the length of each side.
Area of the square = d²/2
here "d" stands for length of diagonal.
Side length of square = (1/4) x perimeter of square
Now let us see some example problems to understand this topic.
Example 1 :
Find the area of the square having side length 24 cm.
Area of the square = a² = 24²
= 24 x 24
= 576 cm²
Hence, area of square is 576 cm²
Example 2 :
A square is of area 64 cm². Then find its side length.
Area of the square = 64 cm²
a² = 64 cm²
a = √64
= √8 x 8 ==> 8 cm
Hence, side length of square is 8 cm
Example 3 :
The square having side length 25 cm. Find the area in meter.
Area of the square = a² = 25²
= 25 x 25 ==> 625 cm²
100 cm = 1 m
= 625/100 ==> 6.25 m²
Example 4 :
Find the area of the square whose diagonal is measuring 4cm.
The diagonal AC divides the square into two right triangles.Δ ACB and Δ ADC. In triangle ACB right angle is at B.
So the side which is opposite to right angle is called as hypotenuse.
By using Pythagorean theorem
AC² = AB² + BC²
4² = x² + x²
16 = 2x²
8 = x²
√8 = x
√2 x 2 x 2 = x
2√2 = x
Therefore, the length of each side is 2√2 cm
Area of the square = a²
= 4 (2)
= 8 cm²
Example 5 :
The diagonals of two squares are in the ratio 2:5. Find the ratio of their area.
Let the diagonals of two squares be 2x and 5x respectively.
Area of a square when diagonal is given = (1/2) x d²
Area of first square = (1/2) x (2x)²
= (1/2) x 4x² ==> 2x²
Area of second square = (1/2) x (5x)²
= (1/2) x 25x² ==> 25x² / 2
Ratio of their areas ==> 2x² : (25x² / 2)
= 4 : 25
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