## 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:**

*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

**Trapezium (Trapezoid) :**

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:**

Area of parallelogram = bh

Perimeter of parallelogram = 2 ( b+ h)

**Rectangle:**

Area of the rectangle = bh

Perimeter of the rectangle = 2 (b + h)

Length of diagonal ( l ) = √ b^{2} + h^{2}

**Rhombus:**

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 :**

Here length of the side for square ABCD = a

Length of diagonal = d = √2 a

Area of the square = b^{2}

Area of the square ABCD = (1/2) d^{2}

Perimeter of the square = 4b

**Kite:**

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:**

Here Origin of the circle = O , Diameter = D and Radius = r

Area of a circle (A ) = π r ^{2} =( π/4 ) D^{2} = 0.7854 D^{2}

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:**

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:**

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 ^{2 }+ ( 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:**

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:**

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:**

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 :**

Here Major axis length Minor axis length

*Area of an Ellipse*

*Perimeter of an Ellipse*** =
**

### 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

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## 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