Diagonal Formula

Diagonal Formula is the formula that is used to find the length of the diagonal of any polygon. There is no one particular formula used to find the length of the diagonals we use different methods to find the length of the diagonal of the polygon.

The number of diagonals that any n-sided polygon has is given using the formula,

Number of Diagonals = n(n-3)/2

This is also called the diagonal formula.

Diagonal Formula For Square

The diagonal of the Square is the line formed by joining two opposite vertices of the square. The formula for finding the length of the diagonal of the square is,

Square Diagonal: a√(2)

where,

• a is the Length of Side of Square

The diagonal of a square is shown in the image added below,

Here, suppose the length of side AB = BC be “a units” then the length of diagonal AC is “a√(2) units”.

Diagonal Formula For Rectangle

The diagonal of the Rectangle is the line formed by joining two opposite vertices of the rectangle. The formula for finding the length of the diagonal of the rectangle is,

Rectangle Diagonal: √[l² + b²]

where,

• l is the Length of Rectangle
• b is the Breadth of Rectangle

The diagonal of a rectangle is shown in the image added below,

Here, suppose the length of side AB = l units, BC = b units then the length of diagonal AC is “√[l² + b²] units”.

Diagonal Formula of Rhombus

The diagonal of the Rhombus is the line formed by joining two opposite vertices of the rhombus. The formula for finding the length of the diagonal of the rhombus is,

p = 2A/q OR q = 2A/p

Where,

• p and q are Diagonals of Rhombus
• A is Area of Rhombus

The diagonal of a rhombus is shown in the image added below,

Here, suppose the area of the rhombus is A units² and its diagonal BD is ‘p’ units then length of its other diagonal AC is, 2(A)/p.

Diagonal Formula of Parallelogram

The diagonal of the Parallelogram is the line formed by joining two opposite vertices of the parallelogram. The formula for finding the length of the diagonal of the parallelogram is,

p = √(x² + y² – 2xycos A) = √(x² + y² + 2xycos B)

q = √(x² + y² + 2xycos A) = √(x² + y² – 2xycos B)

Where,

• p² + q²=2(a² + b²)
• x and y are Sides of Parallelogram
• p and q are Two Diagonals of Parallelogram

Read More,

• Types of Polygons
• Polygon Formula
• Pythagoras Theorem
• Diagonal Formula of Cube

Diagonal Formula is the formula that is used to calculate the length of the diagonal of any polygon. A diagonal is a slant line that joints two alternate sides of any polygon and finding its length is very important for solving various problems of geometry.

There are different ways for finding the diagonal of any polygon and we use various techniques for that purpose. Using Pythagoras Theorem is one such way. We have to study the Diagonal Formula in Class 8. In this article, we will learn about the Diagonal definition, its formula, various examples, and others related to it.