In this page provided formulas of Perimeter and Area for two dimensional geometrical figures like square, rectangle, Rhombus, parallelogram, trapezium or trapezoid, triangle, right angle triangle, ellipse, circle, sector of a circle, segment of a circle etc

Formulas for Two Dimensional Geometrical Figures

Square

Side for square = a  &  Length of diagonal = d

Area of the square = A = side²  = a²  = (1/2) d²

Perimeter of the square = P = 4 × side = 4 a

Length of diagonal = d =

Rectangle

Perimeter of the rectangle = 2 × (length + width) = 2 (a + b)

Area of the rectangle = length × width = ab

Length of diagonal  ( d )   = √ (a² + b²)

Rhombus

For Rhombus all sides are equal = a, Vertical Height = d &  h1, h2 are the diagonals  also  AB || DC , AD || BC

Perimeter of rhombus = 4a

Area of the Rhombus = ad = (1/2) d1 d2

Parallelogram

Area of  parallelogram = base × height = a x h

Perimeter of  parallelogram = 2 × (side1 + side2) = 2 ( a + b)

Trapezium (Trapezoid)

In trapezium  two sides are in parallel,

Area of  Trapezium  or Trapezoid =

Perimeter of Trapezium  or Trapezoid =

Triangle

Formulas for triangle

Area of the triangle = (1/2) x Base x Height = 

Area of the triangle =

Where Semi perimeter =

Radius of incircle triangle = Area /S

Formulas for equilateral triangle

Perimeter of the equilateral triangle = 3 x Side = 3a

Area of the equilateral triangle  =   = 0.433 x (side) ²

Radius of circumference circle of an equilateral triangle =   =   

Area of circumference circle of an equilateral triangle = 

Radius of incircle of an equilateral triangle =   =   a / (2 √3)

Formulas for Right Angle Triangle & Formula for length of a triangle when given by one side and angle

In above figure ABC is a right angle triangle x = length of adjacent side, y = length of hypotenuse & h = height of the triangle.

Pythagoras’ Law – 

Area of the right angle triangle =

Sin β = h / y  ⇒  h  = y  Sin β

Cos β = x / y  ⇒  x  = y  Cos β

Tan β = h / x ⇒  h  = x Tan β

Cosine Law

c ² = a ² + b ² – 2 ab Cos γ

b² = a² + c² – 2 ac Cos β

a² = b2 + c² – 2 bc Cos α

Sine Law    

Area of a Triangle

Circle

Formulas for Area and circumference of the circle

Area of a circle (A ) =  π x (Radius) ²   =  π r ² = ( π/4 ) D² = 0.7854 x D²

Diameter of a circle (D) = 

Circumference of a circle ( C ) = 2 π x Radius =  2 π r = π D

Area of circle =( 1/2) x Circumference x radius = (1/2) x C x  r

Formula for Arc and sector of a circle

Arc length  of circle ( l ) =  

Area of the sector (minor) =

If the angle θ is in radians mean   one radian = 180/π  , then

The area of the sector = 

Sector angle of a circle θ = 

Segment of circle and perimeter of segment

Area of the segment =

Perimeter of the segment =

Arc  Length of the circle segment   =  l  = 0.01745 x r x θ

Chord length of the circle =   =

Area of the circular ring

Area of a circular ring  = = (π/4)  ( D ² – d ²)   = 0.7854 (D ² – d ²)

Area of a circular ring  = π (R ² – r ² )

Ellipse

D = Diameter of higher half-axis & d = Diameter of lower half-axis

Area of an Ellipse =    = 0.7854 x D x d

D = 2 x radius = 2 m , d = 2 x radius = 2 n

Perimeter of an Ellipse (Formula – 1) ≈

Perimeter of an Ellipse (Formula – 2)  ≈

Both formulas gives approximate values but the formula- 2 gives better approch which is derived by Indian mathematician Ramanujan

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