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# Square Properties

### Few Important things to Remember

You all know that math portion is very much important in competitive exams. That doesn’t mean that other topics are less important. But only math portion can leads you to a good score. You can get good score only by practicing more and more. All you need to do is to do math problems correctly within time, and only shortcut tricks can give you that success. But it doesn’t mean that you can’t do math problems without using any shortcut tricks. You may do math problems within time without using any shortcut tricks. You may have that potential.

But, so many other people may not do the same. So Square shortcut tricks here for those people. We always try to put all shortcut methods of the given topic. But we may miss few of them. If you know anything else rather than this please do share with us. Your help will help others.

### What is square?

In a geometry, Square is a regular quadrilateral and This means that it has four equal sides and four equal angles Each angle is holds 90-degree angles, or right angles of each facing side is equal to the opposite side and the square properties are follows.

In maths exam papers there are two or three question are given from this chapter. This type of problem are given in Quantitative Aptitude which is a very essential paper in banking exam. Under below  given some more example for your better practice.

### Square Properties

The two adjacent sides have equal length of Rectangle.

If the length of a rectangle as L of each side then,

a : Area of Square = 4L2 or ( side )2 = 1 / 2 = ( Diagonal ) 2.
The area can also be calculated using the diagonal d according to
A = D2 / 2

Perimeter of a Square = 4L or 4 x Side .
The circumference R, the area of a square is
A = 2R2

b : A room has four wall and its Area of 4 wall is 2 x ( Length + Breadth ) x Height.

c : Area of parallelogram = ( Base  x Height ).

d : Area of a rhombus = 1 / 2 x ( product of diagonals ).

### Example #1 – Square Properties

The area of rectangle is 720 cm2, that is 80% of the area of a square. Find perimeter of the square?

1. 100 cm
2. 120 cm
3. 140 cm
4. 160 cm

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How to Solve
80% of the area of a square is 100 x 720 / 80 = 900cm2.
Side of square is =√900 = 30cm.
Perimeter of square is = 30 x 4 = 120 cm.
Rough Workspace

### Example #2 – Square Properties

The area of square is fourth the area of a rectangle. If the area of the square is 256 sq.cm and the length of the rectangle is 16 cm, then what is the difference between the breadth of the rectangle and the side of the square?

1. 12 cm
2. 16 cm
3. 22 cm
4. 29 cm

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How to Solve
Area of square = 256 sq.cm
Side = 16 cm.

Area of rectangle = 256 / 4 = 64 cm2
l x b = 64
16 x b = 64
b = 4 cm.

Difference between breadth of the rectangle and the side of the square = (a – b) = (16 – 4) = 12 cm.

Rough Workspace

### Example #3 – Square Properties

If the length of the diagonal of a square is 6 meter, then what is length of it’s each side?

1. 3√2
2. 2√3
3. 3√4
4. 4√2

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How to Solve
Side = Diagonal / √2
6 x √2 / √2 x √2
= 3√2.
Rough Workspace

### Example #4 – Square Properties

The area of a rectangle is 18 meters 2 decimeters long and 15 meters 3 decimeters wide. What would be the area of square?

1. 205.27 sq.meters
2. 237.83 sq.meters
3. 257.86 sq.meters
4. 278.46 sq.meters

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How to Solve
Length = 18.2 meters.
So, the area of square is ( Length x Breadth ) = 18.2 x 15.3 = 278.46 square meters.
Rough Workspace

### Example #5

A hall room has the floor which is 30 meters long and 10 meters broad. So, how many meters of cotton carpet of 75 cm wide will be required to cover the room of hall and how much amount will require to be spent on cotton carpet if available at Rs.25/- per meters?

1. Rs.6500/-
2. Rs.8000/-
3. Rs.10000/-
4. Rs.12000/-

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How to Solve
Length required = ( length of room x breadth of room / width of carpet )
= ( 30 x 10 / 75 )
= 400.

Amount = rate per meter x ( length of room x breadth of room / width of carpet )
or, 25 x ( 30 x 10 / 75 )
or, 25 x 400
therefore, 10000.