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.
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
Square Parallelogram |
Rectangle Rhombus |
Traingle Quadrilateral Sector
Hollow cylinder Sphere Area around circle Area of combined figures |
Trapezium Circle Semicircle Quadrant Cyclinder Cone Hemisphere Path ways |
After having gone through the stuff given above, we hope that the students would have understood "Area of a square"
Apart from the stuff given above, if you want to know more about "Area of square", please click here.
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
WORD PROBLEMS
HCF and LCM word problems
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
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