PERIMETER OF SQUARE

In this page perimeter of square we are going to see some example problems to understand this topic. A shape which is having four equal sides is called a square.Now let us see the formula to find perimeter of square.

Formula:

Perimeter of a square = a + a + a + a

= 4a

Example 1:

Find the perimeter of the square having side length 24 cm

Solution:

Perimeter of a square = 4a

here a  =  24 cm

=  4 ( 24 )

=  96 cm

Hence, perimeter of the square is 96 cm

Example 2:

Find the perimeter of the square having side length 15 cm

Solution:

Perimeter of a square = 4a

here a = 15 cm

= 4 ( 15 )

= 60 cm

Therefore perimeter of the square is 60 cm

Example 3:

A square is of area 64 cm². What is its perimeter?

Solution:

Area of a square = 64 cm²

a² = 64 cm²

a = √ 64

a = √8 x 8

a = 8 cm

Now we have to find the perimeter

Perimeter of the square = 4a

= 4 (8)

= 32 cm

Therefore perimeter of the square is 32 cm

Example 4:

Perimeter of a square is 20 cm. What is its area?

Solution:

Perimeter of a square  =  20 cm

4a = 20 ==> a  =  5 cm

Area of a square = a²  =  5² ==> 25 cm²

Therefore area of the square is 25 cm²

Example 5:

Find the perimeter of the square whose diagonal is measuring 4cm.

Solution:

In the above square we have two right triangles. Those are ⊿ ACB and ⊿ ADC. In ⊿ ACB right angled at B. The side which is opposite to this angle is called hypotenuse side. We can find the other sides using Pythagorean theorem.

AC²  = AB² + BC²

Since all sides are equal in square the sides AB and BC are equal in length.

Let AB = x so BC = x

AC² = x² + x²  ==>  4² = 2x² ==>  x² = 16/2 ==>  x² = 8

x = √8

x = √2 x 2 x 2

x = 2 √2 cm

Hence, length of all sides = 2 √2 cm

Perimeter of square = 4a

= 4 (2 √2)

= 8 √2 cm

Example 6:

The perimeter of two squares are 40 cm and 32 cm. Find the perimeter of third square whose area is equal to the difference of the area of two squares.

Solution:

Let "a" and "b" are side length of first and second squares respectively.

Perimeter of first square = 40 cm

4 a  =  40 ==> a  =  10

Perimeter of second square = 32 cm

4 b  =  32 ==> b  =  8

Area of third square  =  10 ²   -  8²  ==> 36 cm²

Side length of third square  =  √36 ==> 6 cm

Perimeter of third square = 4 (6) = 24 cm

More shapes

 Square Parallelogram Rectangle Rhombus Traingle Quadrilateral Area of quadrilateral Sector Hollow cylinder Sphere Area around circle Area around circle example problems Area of combined figures Example problems of area of combined figures Trapezium Area of trapezium Circle Semicircle Quadrant Example problems on quadrant Cyclinder Examples problems of cylinder Cone Hemisphere Example problems of hemisphere Path ways Area of path ways

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

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Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

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Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

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

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6