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Today we are going to talk about some important arithmetic formulae on square , rectangle , quadrilateral , parallelogram , trapezium and rhombus. we are giving whole complete list of all the formulae here ,which are very helpful to solve the problems quickly and accurately. These are very important topics of mensuration , so it is advised to students that they learn these formulae and keep practicing with it.

**SOME IMPORTANT SUTRAS**

*** SQUARE**

1). Area of square = side^2

2). Area of square = diagonal^2/2

3). Diagonal of square = side√2

4). Perimeter of square = 4×side

5). Side of square = √Area

6). Side of square = diagonal/√2

7). Side of square = perimeter/4

8). Diagonal of square = area√2

*

**RECTANGLE**1). Area of rectangle = length × breath

2). Perimeter of rectangle = 2(l+b)

3). Diagonal of rectangle = √l^2+b^2

4). Length of rectangle = A/b

5). Breath of rectangle = A/l

6). Perimeter of rectangle = 2√(2A+d^2)

7). Longer side of rectangle =

√(2A+d^2)+(√d^2-2A)/2

8). Shorter side of rectangle =

√(2A+d^2)-(√d^2-2A)/2

9). If difference between side and the diagonal of the rectangle is given then area of rectangle is =

[d^2-(diff..)^2]/2

10). Area of four wall = 2(l+b)h

*

**QUADRILATERAL**1). Area of quadrilateral = d(p1+p2)/2

2). If diagonal of quadrilateral bisect each other at 90° then area of quadrilateral = d1×d2/2

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**PARALLELOGRAM**1). Area of parallelogram = b×h

2). If θ is the angle between the two side of parallelogram a and b then area = absinθ

3). Perimeter of parallelogram = 2(l+b)

4). Breadth of parallelogram = A/h

5). Height of parallelogram = A/b

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**TRAPEZIUM**1). Area of trapezium = (a+b)h/2

2). Height of trapezium = 2A/a+b

3). If two parallel side of trapezium is a and b and non parallel side is x and y then area of trapezium = (a+b/d)√s(s-x)(s-y)(s-d), where is d is difference of parallel side and s is x+y+d/2.

4). Height of trapezium =

2(a+b/d)√s(s-x)(s-y)(s-d)/a+b

5). Height of trapezium = 2√s(s-x)(s-y)(s-d)/(b-a)

*

**RHOMBUS**1). Area of rhombus = d1×d2/2

2). If rhombus has side a and it’s height is h then area = a×h

3). If θ is the angle between two side of rhombus then it’s area = a^2.sinθ

4). Side of rhombus = 1/2.√(d1^2+d^2)

5). Height of rhombus = d1.d2√(d1^2+d^2)

6). If one side of rhombus is a and it’s one diagonal is d1 then other diagonal = √(4a^2-d1^2)

7). Height of rhombus = d1/2a.√(4a^2-d1^2)

8). If the sum and difference of diagonal of rhombus is S and D then area of rhombus =

(S^2-D^2)/8

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