Two dimensional shapes formulas of area and perimeter calculation

Formulas for two dimensional | Triangle, Quadrilateral, Circle

What is two dimensional shape

A shape with only having two dimensions of width and height and not having another dimension like thickness then it is called two dimensional shape. For example  Circles, Triangles, rectangle, Squares, … etc are called two dimensional objects.

Two dimensional shape also known as “2D”.

In this article cover maximum all two dimensional shapes propertied with formulas of area and perimeter calculations.

Formulas of a Triangle:

Formulas for two dimensional | Triangle, Quadrilateral, Circle

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

Area of the triangle ABC = (1/2) x  a x h

For more concepts regarding the triangles please go through the below link

Classification according to angle and according to sides like Equilateral, isosceles, Scalene, acute angled triangle, Right angled triangle and obtuse angled triangle etc.  | Properties of the Triangles

 

Trapezium (Trapezoid) :

Formulas for two dimensional | Triangle, Quadrilateral, Circle

Here AD || BC ,  Height from base AD to base BC is ” h”  and length of AD = a and BC = b

Then Area of  Trapezium (Trapezoid)  ABCD = (1/2 ) (a + b) h.

 

 

Parallelogram:

Formulas for two dimensional | Triangle, Quadrilateral, Circle

Area of  parallelogram =  bh

Perimeter of  parallelogram = 2 ( b+ h)

 

 

Rectangle:

Formulas for two dimensional | Triangle, Quadrilateral, Circle

 

Area of the rectangle = bh

Perimeter of the rectangle = 2 (b + h)

Length of diagonal  ( l )   = √ b2 + h2

 

Rhombus:

Formulas for two dimensional | Triangle, Quadrilateral, Circle

 

Here height,   AB = BC = CD = DA = b & AB || DC , AD || BC

are the diagonals

Area of the Rhombus ABCD = bh

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

Perimeter of rhombus = 4b

 

 

Square :

Formulas for two dimensional | Triangle, Quadrilateral, Circle

Here length of the side for square ABCD = a

Length of diagonal = d = √2  a

Area of the square = b2

Area of the square ABCD = (1/2) d2

Perimeter of the square = 4b

 

Kite:

Formulas for two dimensional | Triangle, Quadrilateral, Circle

Here BC = DC = a & AB = AD = b

d1 is the length of a diagonal.

d2 is the length of the other diagonal.

Area of kite = (1/2) d1 d2.

 

 

 

 

For more concepts regarding the Quadrilateral please go through the below link

Types of Quadrilateral | Quadrilateral Properties

Area and circumference of a circle:

Formulas for two dimensional | Triangle, Quadrilateral, Circle | Circle formulas in math | Area and circumference of the circleHere Origin of the circle = O , Diameter = D and Radius = r

Area of a circle (A ) = π r 2 =( π/4 ) D2 = 0.7854 D2
Circumference of a circle ( C ) = 2 π r = π D.

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

A = (1/2) x C x  r

Diameter of a circle (D) = √(A/0.7854).

Arc and sector of a circle:

Circle formulas in math | Arc and sector of a circle | Formulas for two dimensional | Triangle, Quadrilateral, Circle

Here angle between two radii is ” θ” in degrees. . And sector of a circle AOB.
Arc length  of circle( l ) (minor) =  ( θ /360) x 2 π r = θ π r / 180

Area of the sector (minor) = ( θ /360) x π r 2

If the angle θ is in radians, then

The area of the sector = (θ/2) r 2

Sector angle of a circle θ = (180 x  l )/ (π r ).

Segment of circle and perimeter of segment:

Circle formulas in math | Area of the circular ring | Formulas for two dimensional | Triangle, Quadrilateral, Circle

Here radius of circle = r , angle between two radii is ” θ” in degrees.

Area of the segment of circle = Area of the sector – Area of ΔOAB.

Area of the segment = ( θ /360) x π r +  ( 1 /2) x  sinθ  x r 2

Perimeter of the segment = (θ π r / 180) + 2r sin (θ/2).

Chord length of the circle =  2  √ [ h (2r – h ) ]

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

Online calculator for circle segment area calculation

Area of the circular ring:

Circle formulas in math | Area of the circular ring | Formulas for two dimensional | Triangle, Quadrilateral, Circle

Here big circle radius = R and Dia = D,

Small circle radius = r and Dia = d,

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

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

Formula for intersecting chords in circle:

Circle formulas in math | Formula for intersecting chords in circle | Formulas for two dimensional | Triangle, Quadrilateral, Circle

Here AB and CD are two chords in circle and intersecting each at the point E.

Then AE : EB = DE : EC.

 

 

 

Formula for length of the tangents of circles:

Circle formulas in math |Length of the tangents of circles | Formulas for two dimensional | Triangle, Quadrilateral, Circle

Here Two circles origins O & O’  and radius are r1 and r2 respectively.

Direct common tangent  AB &  transverse common tangent = CD

Length of  direct common tangent AB = √ [ (Distance between two origins)2 – (r1 -r2)2 ]

= √ [ (OO’)2 – (r1 -r2)2 ]

Length of transverse common tangent AB = √ [ (Distance between two origins)2 – (r1 +r2)2 ]

= √ [ (OO’)2 – (r1 +r2)2 ]

For more concepts regarding the circles please go through the below link

Properties of  circle in math |  Arc, Perimeter, Segment of circle

Area and perimeter of an Ellipse :

Formulas for two dimensional | Triangle, Quadrilateral, Circle, Ellipse

Here Major axis length Minor axis length

Area of an Ellipse

Perimeter of an Ellipse =

 

Two dimensional shapes formulas of area and perimeter calculation

Math Geometry :

Properties of  circle in math |  Arc, Perimeter, Segment of circle

Quadrilateral Properties | Trapezium, parallelogram, Rhombus

Types of Triangles With examples | Properties of  Triangle

Hi friends Thanks for reading. I Hope you liked it. Give feed back, comments and please don’t forget to share it.

Post Author: sivaalluri

My self Sivaramakrishna Alluri. Thank you for watching my blog friend

2 thoughts on “Two dimensional shapes formulas of area and perimeter calculation

    Harish. P

    (June 26, 2018 - 3:45 pm)

    Good information😊👍

      sivaalluri

      (July 3, 2018 - 5:46 pm)

      Thank you Mr.Harish. P

Leave a Reply

Your email address will not be published. Required fields are marked *