AREA OF SQUARE
On this webpage area of square, we are gong to see how to find area of the given square.
Ways to find area of 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 when side length of square is given:
Area of the square = a²
Here "a" stands for the length of each side.
How to find area of square if diagonal is given?
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Area of the square = d²/2 here "d" stands for length of diagonal. |
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How to find the area of a square when perimeter is given?
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.
Solution:
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.
Solution:
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.
Solution:
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.
Solution:
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
= (2√2)²
= 2²(√2)²
= 4 (2)
= 8 cm²
Example 5:
The diagonals of two squares are in the ratio 2:5. Find the ratio of their area.
Solution:
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
More shapes
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Square  Parallelogram  |
Rectangle  Rhombus  |
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Traingle  Quadrilateral  Sector 
Hollow cylinder  Sphere  Area around circle  Area of combined figures  |
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Domain and range of rational functions with holes
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Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
