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** = **side ^{2} = a^{2 } = (1/2) d^{2}**

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 ) **= √ (a ^{2} + b^{2})**

### 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

b^{2} = a^{2} + c^{2} – 2 ac Cos β

a^{2} = b2 + c^{2} – 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 ) D^{2} = 0.7854 x D^{2}**

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

## Pankaj kumar

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

## siva alluri

(December 2, 2022 - 2:44 pm)welcome