25 AUG

Perimeter and Area Formulas for two dimensional geometrical figures

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

Contents

Formulas for Two Dimensional Geometrical Figures

Square

Area of the square, Perimeter of the square, Length of diagonal and Perimeter of the square- sugarprocesstech

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 = a \sqrt{2} \ = \ \sqrt{2 \times \ A } = \ \frac{P}{4} \sqrt{2}

 

Rectangle

Area of the rectangle, Perimeter of the rectangle, Length of diagonal and Perimeter of the rectangle- sugarprocesstechPerimeter of the rectangle = 2 × (length + width) = 2 (a + b)

Area of the rectangle = length × width = ab

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

Rhombus

Formulas for Area of the Rhombus, Perimeter of the Rhombus - sugarprocesstechFor 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

Formulas for Area of the parallelogram, Perimeter of the parallelogram - sugarprocesstech

Area of  parallelogram = base × height = a x h

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

 

 

Trapezium (Trapezoid)

Formulas for Area of the Trapezium or Trapezoid, Perimeter of the Trapezium or Trapezoid - sugarprocesstech

In trapezium  two sides are in parallel,

Area of  Trapezium  or Trapezoid = \frac{1}{2} \ (a+b)h

 

Perimeter of Trapezium  or Trapezoid = a + b + h \left [ \frac{1}{sin\alpha} + \frac{1}{sin \beta} \right ]

Triangle

Formulas for Area of the Triangle, Perimeter of the Triangle - sugarprocesstechFormulas for triangle

Area of the triangle = (1/2) x Base x Height =  \frac{ 1 }{2} \times \ a \times \ h

Area of the triangle = \sqrt{S(S-a)(S-b)(S-c)}

Where Semi perimeter = S = \frac{a+b+c}{2}

Radius of incircle triangle = Area /S

Formulas for equilateral triangle

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

Area of the equilateral triangle  =  \frac{\sqrt{3}}{4} \times (Side )^2  = 0.433 x (side) 2

Radius of circumference circle of an equilateral triangle = S = \frac{Side \ ^3}{4\times Area \ of \ Triangle}  =    \frac{a}{\sqrt{3}

Area of circumference circle of an equilateral triangle =  \pi \times \left ( \frac{a}{\sqrt{3}} \right )^2

Radius of incircle of an equilateral triangle = = \frac{ Area \ of \ Triangle}{ Semi \ perimeter (S) }  = \frac{a}{2\sqrt{3}  a / (2 √3)

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

Formulas for Area of the right angle Triangle, Perimeter of the right angle Triangle - How to find length of a triangle given one side and angle-sugarprocesstech

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 –  x^2 + h^2 = y^2

Area of the right angle triangle = \frac{1}{2} xh

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     \frac{a}{sin \ \alpha} = \frac{b}{sin \ \beta} = \frac{c}{sin \ \gamma}

Area of a Triangle

\frac{b \ c \ sin \ \alpha}{2} = \frac{a \ c \ sin \ \beta}{2} = \frac{a\ b \ sin \ \gamma}{2}

Circle

Circle Formulas, Area of a circle , Circumference of a circle, Arc and sector of a circle, Segment of and perimeter of segment in a 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) = \sqrt { \frac{Area \ of \ a \ circle}{0.7854}}

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 ) =   \frac{ \theta }{360} \times 2\pi r \ = \ \frac{ \theta \ \pi r }{180}

Area of the sector (minor) = \frac{ \theta }{360} \times \pi r^2 \

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

The area of the sector =  \frac{ \theta }{2} \times r^2 \

Sector angle of a circle θ =  \frac{ 180 \times l }{\pi r}

Segment of circle and perimeter of segment

Area of the segment = \left ( \frac{\theta}{360} \right )\pi r^2 \ -\ \left ( \frac{1}{2} \right ) \ sin\theta \ r^2

Perimeter of the segment = \left ( \frac{\theta \ \pi \ r }{180} \right ) \ -\ 2r \ sin\theta \ \left ( \frac{\theta}{2} \right )

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

Chord length of the circle = \ 2r \ sin\theta \ \left ( \frac{\theta}{2} \right )  = 2 \ \sqrt{h (2r -h)}

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

Formulas for Area of the Ellipse, Perimeter of the Ellipse - sugarprocesstech

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

Area of an Ellipse = \frac{\pi}{4} \ \times D \times \ d   = 0.7854 x D x d

 

 

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

Perimeter of an Ellipse (Formula – 1) ≈ 2\pi \sqrt{ \frac{m^2 \ + \ n^2 }{2} }

Perimeter of an Ellipse (Formula – 2)  ≈ \pi \ \left [ 3 (m \ + \ n ) - \sqrt{(3m+n) (m+3n)} \right ]

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

Perimeter and Area of 2D geometrical figures of square, rectangle, Rhombus, parallelogram, trapezium or trapezoid, triangle, right angle triangle, ellipse, circle, sector of a circle, segment of a circle etc

 

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Post Author: siva alluri

The aim of this Blog "sugarprocesstech" is Providing basic to advance knowledge in sugar process industry and providing maximum calculation regarding capacity and equipment design online calculators .

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2 thoughts on “Perimeter and Area Formulas for two dimensional geometrical figures”

    Pankaj kumar

    (November 20, 2022 - 3:43 pm)
    Reply

    Good

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