Home » Area and Perimeter
Math Formulas Basic | Kite

Smart Math Formula KiteSmart Math Formula, A kite is a quadrilateral with two pairs of adjacent sides that are congruent. The diagonals of a kite are perpendicular.
 

Smart Diagonal Method : Area of Kite = ½ . d1 . d2
Smart Trigonometry Method : Area of Kite = a . b . Sin C
Perimeter of Kite = 2[a + b]
 
Note :
a = length, b = breadth, d1, d2 are diagonals
                                              

Example

Question : Find the area of a kite with the given diagonals 2, 4 using Smart Diagonal Method.
Answer : Find the area.
Area = ½ . d1 . d2 = 0.5 . 2 . 4 = 4.


Question : Find the area of a kite with the given length 2 and breadth 3 using Smart Trigonometry Method.
Answer : Find the area.
Area = a . b . Sin C = 2 . 3 . Sin(33) = 6 . 1 = 6.


Question : Find the perimeter of a kite with the given length 2 and breadth 3.
Answer : Find the perimeter.
Perimeter = 2[a + b] = 2.[2 + 3] = 2.[5] = 10.


That is example will clearly illustrates how to calculate the Area and Perimeter of a Kite Smart Math Formula.

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Math Formulas Basic | Circle

Smart Math Formula Circle
Smart Math Formula Circle,  A circle is a certain distance from the point to the so-called rotating circle, whose name is the diameter (d) is the diameter and the radius [ r ] is half of the diameter.

Wide circle = πr ²
Diameter of circle = 2r
Circumference of circle= 2πr= πd
                                      Sector wide = πr x [θ/360]

Note :
r = radius , d = diameter , ∏ = 3.14 or 22/7 [ if radius and diameter can divided 7 ]   

Example

Question : Find the area, diameter and circumference of a circle with the given radius 3.

Answer: Find the area.
Area = πr² = 3.14 x 3² = 3.14 x 9 = 28.26.

Answer: Find the diameter.
Diameter = 2r = 2 x 3 = 6.

Answer: Find the circumference.
Circumference = πd = 3.14 x 6 = 18.84.

Question : Find the area of sector with the given radius 3 and theta 30.

Answer: Find the area.
Area =πr²(θ/360) = 3.14 x 3² x (30/360) = 3.14 x 9 0.083 = 2.35.

That is example will clearly illustrates how to calculate the Area, Diameter and Circumference of a Circle, Area of Sector with Smart Math Formula way.

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Math Formula Basic | Kite

Smart Math Formula KiteSmart Math Formula, A kite is a quadrilateral with two pairs of adjacent sides that are congruent. The diagonals of a kite are perpendicular.
 

Smart Diagonal Method : Area of Kite = ½ . d1 . d2
Smart Trigonometry Method : Area of Kite = a . b . Sin C
Perimeter of Kite = 2[a + b]
 
Note :
a = length, b = breadth, d1, d2 are diagonals
                                              

Example

Question : Find the area of a kite with the given diagonals 2, 4 using Smart Diagonal Method.
Answer : Find the area.
Area = ½ . d1 . d2 = 0.5 . 2 . 4 = 4.


Question : Find the area of a kite with the given length 2 and breadth 3 using Smart Trigonometry Method.
Answer : Find the area.
Area = a . b . Sin C = 2 . 3 . Sin(33) = 6 . 1 = 6.


Question : Find the perimeter of a kite with the given length 2 and breadth 3.
Answer : Find the perimeter.
Perimeter = 2[a + b] = 2.[2 + 3] = 2.[5] = 10.


That is example will clearly illustrates how to calculate the Area and Perimeter of a Kite Smart Math Formula.

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Math Formula Basic | Polygon

Smart Math Formula, A polygon is a plane figure that is bounded by a closed path or circuit, composed of a finite sequence of straight line segments.


Formula length of a side :
Area of Polygon = {[ side ]² . N] / [4.Tan(π / N]}
Perimeter of Polygon = N . [side]

Formula radius (circumradius) :
Area of Polygon = ½ . R² . Sin[2.π / N]

Formula apothem [inradius] :
Area of Polygon = A² . N . Tan(π / N)
where A = R . Cos(π / N)

Formula apothem and length of a side :
Area of Polygon = [A x P] / 2
where A = side / [2 x Tan(π / N]

Note :
N = Number of sides, A = Apothem, R = Radius, P = Perimeter


Example 

Question : Find the area and perimeter of a polygon with the length 2 and the number of sides is 4.

Smart Math Formula : Find the area.
Area = {[side]² . N] / [4.Tan[π / N]} = {[2]² . 4) / (4 . Tan[3.14 / 4]}
= (4 . 4) / 4 . Tan(0.785)
= 16 / 4 . 0.999
= 16 / 3.996
Area = 4.

Smart Math Formula : Find the perimeter.
Perimeter = [N .[side] = 4 . 2 = 8

Question : Find the area of a polygon with the given radius 2 and the number of sides is 5.
Smart Math Formula : Find the area.
Area = ½ . R² . Sin[2.π / N]
= [0.5] . 2² . Sin(2 . 3.14 / 5]
= 0.5 x 4 x Sin[6.28 / 5]
= 2 x Sin[1.26]
= 2 x 0.95
Area = 1.9.

Question : Find the area of a polygon with the given radius 2 and the number of sides is 5 using Apothem.

Smart Math Formula : Find the apothem.
Apothem = R . Cos[π / N]
= 2 . Cos[3.14 / 5]
= 2 . Cos[0.63]
= 2 . 0.81
Apothem = 1.62.

Smart Math Formula : Find the area.
Area = A² . N .Tan[π / N]
= 1.62² . 5 .Tan[3.14 / 5]
= 2.62 . 5 . Tan[0.63]
= 13.1 . 0.73
Area = 9.5.

Case 4: Find the area of a polygon with the length 2 and the number of sides is 4 using Apothem.

Smart Math Formula : Find the apothem.
Apothem = side / [2 .Tan[π / N] = 2 / [2 . Tan[π / 4]
= 2 / [2 .Tan(0.785]
= 2 / [2 . 0.999]
= 2 / 1.998
Apothem = 1.

Smart Math Formula : Find the perimeter.
Perimeter = [N x [side] = 4 x 2 = 8

Smart Math Formula : Find the area.
Area = [A x P] / 2
= [1 x 8] / 2
= 8 / 2
Area = 4.

That example be smart illustrates how to calculate the Area, Perimeter of a Polygon Smart Math Formula.

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Math Formula Basic | Trapezium

Smart Math Formula TrapeziumSmart Math Formula Trapezium, a trapezium is a shape with four sides, that has one set of parallel sides.
 
Trapezium/Trapezoid :

Area of Trapezium = ½.[a + b].h
 
where  = a, b = sides, h = height 

Perimeter of Trapezium a+b+c+d
 
Note : sides = a, b, c, d  

Example

Trapezium using the sides length a= 6, b=3 and the height 4.
The Area is....
 Question : Find the area. 
Area = ½ . [a + b] . h = ½ . [6 + 3] x 5 = ½ . 9 .4 = 18.
Trapezium using the sides length a= 6, b= 3, c= 4 and d= 6.
The Perimeter is.....
Question : Find the perimeter.
Perimeter = a + b + c + d = 6 + 3 + 4 + 6 = 19.

That example Smart Math Formula Trapezium how to calculate the Area and Perimeter of a Trapezium.

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Math Formula Basic | Rhombus


Smart Math Formula Rhombus,  a Rhombus is a four sided polygon in which every side has the same length. 

Rhombus Formula : It is an equilateral quadrilateral.

Base Times Height Method : Area of Rhombus = b . h

Diagonal Method : Area of Rhombus = ½ . d1 . d2

Perimeter of Rhombus = 4 . [a]

Note :
a = side, b = breadth, h = height, d1, d2 [Are diagonals Rhombus]

Example

Question: Find the area of a rhombus with the given base 6 and height 8 using Base Times Height Method.

Question: Find the area.

Area = b . h = 6 . 8 = 48

Question: Find the perimeter of a rhombus with the given side 6.

Question: Find the perimeter.

Perimeter = 4 . [a] = 4 . 6 = 24.

That example will clearly illustrates how to calculate the Area, Perimeter of a Rhombus manually.

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